Book Description
The theory of distributions is an extension of classical analysis, an area of particular importance in the field of linear partial differential equations. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without a knowledge of this. The material in this book, based on graduate lectures given over a number of years requires few prerequisites but the treatment is rigorous throughout. From the outset, the theory is developed in several variables. It is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces. In this second edition, the notion of the wavefront set of a distribution is introduced. It allows many operations on distributions to be extended to larger classes and gives much more precise understanding of the nature of the singularities of a distribution. This is done in an elementary fashion without using any involved theories. This account will be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics.
Customer Reviews:
An Excellent Introduction.......2000-11-02
Every physicist and mathematician uses distributions (sometimes called generalized functions), albeit often unknowingly. From its origins in the Dirac delta `function', distribution theory continues to influence many research areas from quantum mechanics to partial differential equations, but has also grown into an important field in its own right. For anyone interested in learning about the field, this is clearly the first port of call. It presents a balanced introduction to the subject on a level suitable for anyone with a basic grounding in analysis (no knowledge of functional analysis is required).
The book begins by defining the two building blocks of the theory---test functions and distributions. It then quickly expands, filling in the important details of differentiation, multiplication, tensor products and convolution. All of this is written with sufficient mathematical rigor, but never too much that it interferes with the basic understanding of the subject, and is supported throughout by useful exercises. The book then builds up the theory of Fourier and Laplace transforms of distributions, which has important applications in the study of linear partial differential equations. The second edition contains an indispensable new chapter on the calculus of wavefront sets, which, among its uses, allows the propagation of singularities of solutions to partial differential equations to be properly treated. All in all, while the book is not for the common man, and does require a certain level of mathematical maturity, it does present an excellent introduction to an important, and often poorly understood, area of mathematics.
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Large Sample Methods in Statistics: An Introduction with Applications
Pranab K. Sen , and
Julio M. Singer
Manufacturer: Chapman & Hall/CRC
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Binding: Hardcover
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ASIN: 0412042215 |
Book Description
This text bridges the gap between sound theoretcial developments and practical, fruitful methodology by providing solid justification for standard symptotic statistical methods. It contains a unified survey of standard large sample theory and provides access to more complex statistical models that arise in diverse practical applications.
Book Description
Well-known text provides introduction to distribution theory, describes generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations and passive systems. Numerous problems. Bibliography.
Customer Reviews:
Note on Delta function.......2006-01-12
Just a note for readers of these reviews: there are two delta functions used in signal processing. In digital signal processing the Kronecker delta is used, which is simple. In continuous-time signal processing the Dirac delta is used, which is a generalized function and causes sophomores no end of headaches. Zemanian's book will be helpful for those wishing to know more about generalized functions such as the Dirac delta. Those just wishing to know a little more might find the articles on Wikipedia about Dirac delta more helpful.
Great book.......2004-03-23
This an an excellent, clear book which is widely referenced. It was much clearer than Lighthill to me. I was comfortable with dirac delta functions in the intuitive presentation from my EE linear systems courses, but I needed to understand the theory to do correct proofs for my dissertation. This book filled the gap excellently, while being easy to follow.
This is a good second or third book on generalized functions.......2000-06-17
This is a good second or third book on generalized functions which are otherwise known as "distributions". A good first book is "Fourier Analysis and Generalised Functions" by Lighthill. This book is based on a graduate course and provides a good introduction to distribution theory and generalized Fourier analysis. You need to have a good background in advanced calculus and be comfortable with Lebesgue theorems concerning interchangeable limit processes. The examples are quite good, but the notation is intense and the way that it is packed in small font onto a page doesn't help. The writing is compact and thorough.
I recommend this book to anyone who has had the standard digital signal processing course where the Delta function (distribution) is used freely and who has wondered what it really means.
Book Description
This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes.
Key Topics and Features:
* Solid introduction to analytic number theory, including full proofs of Dirichlet’s Theorem and the Prime Number Theorem
* Solid treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals
* First treatment in book form of the AKS algorithm that shows that primality testing is of polynomial time
* Many interesting side topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers
The book’s user-friendly style, historical context, and wide range of exercises from simple to quite difficult (with solutions and hints provided for select ones) make it ideal for self study as well as classroom use. Intended for upper level undergraduates and beginning graduate students, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced in the book.
Book Description
A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.
This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
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Introduction to the Theory of Distributions (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)
J Campos Ferreira ,
R F Hoskins , and
Jose Sousa-Pinto
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Loose Leaf
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ASIN: 0582311446 |
Book Description
A topic of major importance to engineers and physicists, the theory of distributions remains a difficult subject for the non-mathematician. This version of the theory presents a more natural approach.
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Equidistribution in Number Theory, An Introduction (NATO Science Series II: Mathematics, Physics and Chemistry)
Manufacturer: Springer
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ASIN: 1402054025 |
Product Description
Written for graduate students and researchers alike, this set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos.;
The volume brings together leading researchers from a range of fields, whose accessible presentations reveal fascinating links between seemingly disparate areas.
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Freedom and Security: An Introduction to the Basic Income Debate
Tony Fitzpatrick
Manufacturer: Palgrave Macmillan
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ASIN: 0312223137 |
Book Description
This book offers a refreshing alternative to most texts on the welfare state. The author provides an introduction to the Basic Income debate, while examining a range of arguments. A Basic Income would be an income paid periodically and unconditionally to every man, woman and child as a fundamental right of citizenship and without reference to employment, marital and household status. The author's position is that the principles of collective and universal welfare can be defended but that the system should be reformed by introducing the radical yet disarmingly simple device of Basic Income.
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Generalized Functions and Fourier Analysis: An Introduction (Mathematics lecture note series)
John L. Challifour
Manufacturer: Benjamin-Cummings Pub Co
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ASIN: 0805318755 |
Book Description
This powerful short novel describes the events of a single afternoon. Alwyn Towers, an American expatriate and sometime novelist, is staying with a friend outside of Paris, when a well-heeled, itinerant Irish couple drops in—with Lucy, their trained hawk, a restless, sullen, disturbingly totemic presence. Lunch is prepared, drink flows. A masquerade, at once harrowing and farcical, begins. A work of classical elegance and concision, The Pilgrim Hawk stands with Faulkner's The Bear as one of the finest American short novels: a beautifully crafted story that is also a poignant evocation of the implacable power of love.
Customer Reviews:
Brilliant.......2007-10-09
Several years back, I was given the first 100 of the New York Review Books for Christmas (a much-appreciated, very generous gift!). Sad to say, I have read few of them. But yesterday, browsing my bookshelf, I picked out 'The Pilgrim Hawk,' attracted, no doubt, by the slimness of the volume. After reading it, I have to say that it has been a long time since I have been so impressed by a book - it truly is an unknown classic. And, as an aside, the introduction by Michael Cunningham is wonderful!
I have no knowledge of Glenway Wescott and his other writing, but the execution of this book is flawless. The narrator is someone who stands a bit outside of life, observing. His detachment contrasts with the self-aborption and high emotion of the main characters of the book, an ever-travelling married couple from Britain (the husband is english, the wife is Irish). The entire book occupies just one afternoon, but it is rife with emotion and intense observations on life and love. And Wescott is a talented writer - I continually found myself admiring his phrasing. Here is a quote, which is admittedly depressing, but delights me none-the-less, in which Wescott describes the unfulfilled bachelor (or bachelorette!):
"Life goes on and on after one's luck has run out. Youthfulness persists, alas, long after one has ceased to be young. Love-life goes on indefinitely, with less and less likelihood of being loved, less and less ability to love, and the stomache-ache of love still sharp as ever."
A mixed-genre classic combining interior monologue with the feel of autobiography.......2005-12-20
The plot line of Glenway Wescott's short novel, The Pilgrim Hawk: A Love Story, is quite simple; a wealthy Irish couple, Mr. and Mrs. Cullen, spend an afternoon at the French home of an American friend, Alexandra Henry, and her American house guest, Alwyn Tower. The setting is the late 1920s, and Alwyn Tower is telling the story of the Cullens' visit from a supposedly objective distance, in the early 1940s. Clearly what occurred that day with the Cullens seemed so remarkable that Tower is still thinking of them twelve years later.
The surrealistic feature of the story (which was so bizarre to this reader as to be at first off-putting) is that Madeleine Cullen has a passion for falconry and is traveling with a full-grown peregrine falcon perched on her wrist, a bird which she must take with her everywhere. The "love" story is a triangle: Larry Cullen is in competition with a feathered being for his wife's affection.
Regarding the craft of the novel, the hawk, Lucy, is so palpable on the page that Wescott must have researched hawk behavior and falconry, i.e., hawk-human interaction. But research alone would not have been enough to make any bird a character in a novel; Wescott takes our feathered friends to a higher level of literary metaphor and character.
To have the novel work as a whole, the novelist must employ a structure of writing that maximizes the benefit and entertainment that readers expect. The characteristic quality of The Pilgrim Hawk is that the first-person narrator, Alwyn Tower, is so intelligently perceptive that his viewpoint is almost impossible to distinguish from the single, controlling observer, the omniscient narrator. Tower is the most compassionate of narrators as he sees into both Larry Cullen and Madeleine Cullen, the role of Lucy, as well as the household servants. Such an informed and knowledgeable narrator--who also reveals his own sensitive consciousness--makes me suspect that Alwyn Tower is Glenway Wescott himself. Employing the technique of interior monologue, Wescott reveals Tower's epistemological doubts as Tower filters other's dialogue through his single, though ultimately limited, consciousness. And Wescott's sentences are constructed with such care for the English language that one feels Tower is Wescott.
The NYRB paperback production makes this novel an edition you will want to own: The cover art, by Nam June Paik, is as sophisticated and enigmatic as the relationships in the novel. Aesthetic production features of other books in the NYRB series have included evocative colors on the inside front covers: magenta, peach orange, and royal purple. The inside cover of The Pilgrim Hawk is a hypnotic turquoise. I have never spent so much time gazing at the inside cover of any book as I have of this one.
Informative and insightful introduction by MICHAEL CUNNINGHAM, who as the author of The Hours, a work about Virginia Woolf, is certainly qualified to write about Wescott's "hawklike" observations of human behavior. Cunningham writes, "Almost every page contains some small wonder of phrase or insight, some instance of the world keenly observed and reinvented" (xvii).
on and on and on.......2005-06-04
The writers style needs improvement. The chapters, what chapters, there are no chapters . The book goes on and on and on. It is a difficult book to put down and pick up. Again , no chapters and the characters are too sterile.This book is too classic for me or is a hawk eating dead pigeons a classic story. eugh!
"The old bachelor is like an old hawk.".......2004-09-26
In "The Pilgrim Hawk" American writer, Alwyn Towers, relates the events of one strange afternoon in the late 1920s. Towers is visiting a friend, Alexandra May, at her country home in France when the Cullens, a wealthy married Irish couple, arrive unannounced. The Cullens are "self centered without any introspection, strenuous but emotionally idle." Towers notes that during the twenties, one often came across "foreigners in some country as foreign to them as to you ... and you did your best to know them in an afternoon." Towers certainly does 'get to know' the Cullens who are "mere passers of time" during this brief afternoon, and Towers is able to observe and analyze the strange relationship between the seemingly frivolous Madeleine and her half-inebriated husband.
Madeleine Cullen sports a captive and crippled Pilgrim Hawk--which she wears attached to her wrist. At first, the hawk, named Lucy, seems to be a fetish object for Madeleine. Lucy wears a feathered hood that matches Madeleine's hat, and the manner in which the Cullens demand accommodations for the hawk is rather peculiar. Madeleine, for example, is eager to show off the bird and expects that special arrangements should be made for the bird's dinner. But soon it becomes obvious that the hawk is more than just a fetish object for Madeleine. Madeleine and the hawk are practically inseparable--a fact that Mr. Cullen finds both irritating and nauseating. Is he merely jealous of the attention the hawk receives, or does Cullen's hatred for the hawk have another origin?
Towers relates the events of the lazy afternoon as "something a little sour and dark" creeps into the conversation, and through Tower's observant eyes, it becomes apparent that the hawk represents many things. It is as if Lucy is the third participant in a bizarre love triangle, for she is Madeleine's beloved, and Larry Cullen despises the hawk for this. Just as Lucy is a captive in her relationship with Madeleine, the Cullens are also captive in their unhappy marriage: "when love has given satisfaction, then you discover how large a part of the rest of your life is only payment for it, installment after installment." The Cullens' unhappy marriage seems to fester around the hawk, and as Larry Cullen drinks the afternoon away, simmering resentments develop into a spiteful and desperate act.
"The Pilgrim Hawk" is a short novel, and it is utterly exquisite. Author, Glenway Wescott focuses on the incidents that take place during a few hours, and he reconstructs the afternoon with perfection and skilled descriptive power. The narrator's initial reaction to the Cullens and his subsequent curiosity about their marriage conveys a very personal recollection that is shared between the narrator and the reader. Consequently, one feels as though the narrator, telling the tale 20 years later, has never forgotten the incidents of that one afternoon, and he shares that peculiar and lasting memory with us--displacedhuman
Upstairs, Downstairs in miniature.......2004-06-08
This is an odd little book. The events take place in a single afternoon at the home of an American woman in France between the First and Second World Wars. The narrator, Alwyn Tower, and his hostess, Alexandra Henry, are visited by the Cullens, a middle-aged Irish couple. Mrs. Cullen has brought along her pet hawk Lucy whose presence dominates the remainder of the story (both symbolically and as another character). With its hood on, the hawk seems to represent the blindness of a class of wealthy internationals who live for food and fun, and who have made an uneasy peace with their captivity and lack of freedom.
Meanwhile, a trio of servants (Jean and Eva, the cooks; and Ricketts, the Cullens' chauffeur) plays yang to the aristocats' yin. For them, flirtation, jealousy, and passion are the defining mainstays of their existence. And they don't even need to turn to alcohol to release these life forces.
It's hard to know how seriously we are to take the narrator, a novelist twice failed in love. He is an astute observer and chronicler of the events, but his self-acknowledged failures as a writer certainly seem to justify the uncomfortable feelings he has toward Mrs. Cullen's captive carnivore. Although we know from page one that the Americans Alexandra and Alwyn would eventually return to America when tensions increase in Europe, at the novel's end it seems somewhat doubtful that either one will ever muster the energy needed to leave their perches in Alexandra's parlor.
This short novel has some of the biting class insights of Saki's better stories. Other than that, I find it hard to compare this book to any other I have ever read. Interesting in spite of and because of its brevity. Worth reading and rereading.
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- Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)
- $J$-holomorphic Curves and Symplectic Topology (Colloquium Publications (Amer Mathematical Soc))
- Latent Curve Models : A Structural Equation Perspective (Wiley Series in Probability and Statistics)
- Lattices and Ordered Algebraic Structures (Universitext)
- Lattices and Ordered Algebraic Structures (Universitext)
- Mathematical and Physical Modeling of Materials Processing Operations
- Mathematical Modeling and Optimization: An Essay for the Design of Computer-Based Modeling Tools (Applied Optimization)
- Mathematical Models for Structural Reliability Analysis (Crc Mathematical Modelling Series)
- Mathematical Models in Boundary Layer Theory (Applied Mathematics and Mathematical Computation Series)
- Matrix Groups: An Introduction to Lie Group Theory
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