Semigroups of Linear Operators and Applications to Partial Differential Equations (Applied Mathematical Sciences)

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From the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of the London Mathematical Society#2

Customer Reviews:

The content is optimal, the printing is poor.......2007-03-21

Although the book is a compilation of class notes, it is very well written, and suitable for the level of a second or third year graduate student. The only needed background is strong foundation on functional analysis. The author explain very well how semigroups become the state of the art for applied mathematicians.

On the other side, the printing of the book is very poor, the letters actually tend to disapear in several pages and I'm not the only that went thru this.

Algebra in the Stone-Cech Compactification: Theory and Applications (De Gruyter Expositions in Mathematics, 27) (De Gruyter Expositions in Mathematics)

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Algebra in the Stone-Cech Compactification: Theory and Applications (De Gruyter Expositions in Mathematics, 27) (De Gruyter Expositions in Mathematics)
Neil Hindman , and Dona Strauss
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Hardcover

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ASIN: 311015420X

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A study of the algebraic properties of compact right topological semigroups in general and the Stone-Cech compactification of a discrete semigroup in particular. Several powerful applications to combinatorics, primarily to the branch of combinatorics known as Ramsey Theory, are given. Connections with topological dynamics and ergodic theory are also presented.

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Algebraic Theory of Automata Networks investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories. Automata networks are investigated as products of automata, and the fundamental results in regard to automata networks are surveyed and extended, including the main decomposition theorems of Letichevsky, and of Krohn and Rhodes. The text summarizes the most important results of the past four decades regarding automata networks and presents many new results discovered since the last book on this subject was published. Several new methods and special techniques are discussed, including characterization of homomorphically complete classes of automata under the cascade product; products of automata with semi-Letichevsky criterion and without any Letichevsky criteria; automata with control words; primitive products and temporal products; network completeness for digraphs having all loop edges; complete finite automata network graphs with minimal number of edges; and emulation of automata networks by corresponding asynchronous ones.

Stability and Stabilization of Infinite Dimensional Systems with Applications (Communications and Control Engineering)

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Stability and Stabilization of Infinite Dimensional Systems with Applications (Communications and Control Engineering)
Zheng-Hua Luo , Bao-Zhu Guo , and Ömer Morgül
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 1852331240

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This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robot arms and large space structures. Various control methods such as sensor feedback control and dynamic boundary control are applied to stabilize the equations. Many new theorems and methods are included in the book. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. In addition to benefiting from the presentation of new results on semigroups and their stability, readers can also learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.

Analytic Semigroups and Optimal Regularity in Parabolic Problems (Progress in Nonlinear Differential Equations and Their Applications)

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Analytic Semigroups and Optimal Regularity in Parabolic Problems (Progress in Nonlinear Differential Equations and Their Applications)
Alessandra Lunardi
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover

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ASIN: 3764351721

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The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems.
Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones.
Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived.
The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques.

The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications)

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The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications)
Jan van Neerven
Manufacturer: Birkhauser
ProductGroup: Book
Binding: Hardcover

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ASIN: 3764354550

Book Description

This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.

Co-Semigroups and Applications (North-Holland Mathematics Studies)

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Co-Semigroups and Applications (North-Holland Mathematics Studies)
Ioan I. Vrabie
Manufacturer: JAI Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0444512888

Book Description

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of C o-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-like methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book.

Book Description

Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

The Functional Calculus for Sectorial Operators (Operator Theory: Advances and Applications)

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The Functional Calculus for Sectorial Operators (Operator Theory: Advances and Applications)
Markus Haase
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover

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ASIN: 376437697X

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The present monograph deals with the functional calculus for unbounded operators in general and for sectorial operators in particular. Sectorial operators abound in the theory of evolution equations, especially those of parabolic type. They satisfy a certain resolvent condition that leads to a holomorphic functional calculus based on Cauchy-type integrals. Via an abstract extension procedure, this elementary functional calculus is then extended to a large class of (even meromorphic) functions.

With this functional calculus at hand, the book elegantly covers holomorphic semigroups, fractional powers, and logarithms. Special attention is given to perturbation results and the connection with the theory of interpolation spaces. A chapter is devoted to the exciting interplay between numerical range conditions, similarity problems and functional calculus on Hilbert spaces. Two chapters describe applications, for example to elliptic operators, to numerical approximations of parabolic equations, and to the maximal regularity problem.

This book is the first systematic account of a subject matter which lies in the intersection of operator theory, evolution equations, and harmonic analysis. It is an original and comprehensive exposition of the theory as a whole. Written in a clear style and optimally organised, it will prove useful for the advanced graduate as well as for the experienced researcher.

Infinite Words: Automata, Semigroups, Logic and Games (Pure and Applied Mathematics, Volume 141) (Pure and Applied Mathematics)

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Infinite Words: Automata, Semigroups, Logic and Games (Pure and Applied Mathematics, Volume 141) (Pure and Applied Mathematics)
Dominique Perrin , and Jean-Éric Pin
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0125321112

Book Description

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic.

Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger.

Serves as both an introduction to the field and as a reference book.
Contains numerous exercises desgined to aid students and readers.
Self-contained chapters provide helpful guidance for lectures.

Customer Reviews:

Legendary Tale of Mediocrity.......2007-06-08

I just finished this saga, I have read four others (Njal's Saga, Eyrbyggja Saga, Erik's Saga, Jomsvikings Saga) and it is far shorter than any of those. It boasts of it's legendary people, even of its "knights" and all I kept thinking was Hrolf isn't as much Beowulf as the introduction lends, but as King Arthur. His champions reminded me much of the Knights of the round table, except Bodvar's and Hott's (Hjalti) story which had me riveted. Their tale of being had me going but the other parts seemed to putter along without the cold breeze of wonder and excitement that previous sagas had on me. It reads in the scriber's own day and time and not in the time that the actual events fictiously happened in. The scriber didn't take me back into a frozen wonderland of mystery, vast journeys and people with heart and soul. This is my least favorite saga I've read, but like other reviewers have said, it has a kind of charm that makes you want to see the end of it all. Love it or hate it its only 79 pages of your life and its still worth a read.

An Essential Nordic Legend.......2006-08-22

The mythology and legends of a people portray their philosophy, ideals, morality, and character. This saga takes place mainly in pre-Christian Scandinavia, and is a testament to the heroic nature, and high standards of personal honor idealized by the cultures of Northern Europe. The central character is King Hrolf Kraki, a Danish warrior-king of great status in his region. As is common in most Scandinavian Sagas, the story starts with the ancestors in previous generations, describing how the main characters came to be in the significant circumstances of the narrative. The saga contains the exploits of numerous people, good and evil, noble or corrupt, whose actions result in the plight of the primary heros. It is through the tale of one of these main characters, Bodvar, that we have an insight into the Heroic Ideal of ancient pre-Christian Scandinavians:
Bodvar was a warrior of abnormal strength and courage. He was one of three exceptional brothers, all born with abnormal supernatural attributes due to a spell upon their parents at the hands of an evil sorceress-queen. Bodvar went forth to become a warrior in the service of King Hrolf Kraki. At the court, he found that the favored means of entertainment by the king's champions, was to hurl bones at a week, clownish and pathetic man named Hot. They forced him nightly to sit in the bone-pile, where he was frequently injured by this abusive hazing. Bodvar's sensibilities are outraged by this vile behavior against a defensless person. The champions are mostly a clique of loud-mouthed braggarts. Bodvar enters the hall, speaking to no one. His first action, is to drag Hot out of the bone-pile, and sit him on the bench next to him. All the king's champions are outraged by this audacity, and after some tense silence and hard stares, one of them acquires the nerve to throw a large ox bone at Bodvar. Bodvar catches it, and hurls it right back at the instigator, killing him outright. At this point, the king inquires as to who he is, why he is there. After introductions, Bodvar is welcomed into the king's service. Bodvar retains Hot as a sidekick.
Later on, it has come the time of year when a monster makes his annual visit to kill and eat one of the king's warriors (echos of Beowulf). Bodvar takes Hot out to find this monster, and he kills it outright. Hot, being very mortal, is terrified. Bodvar forces Hot to drink the monster's blood, and then gives him arms, and trains him to fight. Hot undergoes a transformation. At the hall, king Hrolf renames him Hjalti the magnanimous. Together, Bodvar and Hjalti eventually kill off the remaining thugs in the king's service, and recruit better men to serve the king.
This, to me, is the measure of a true hero. A hero can not abide dishonorable behavior, and takes a stand against it. He helps a weak person to be strong, and doing so, creates yet another hero.

Exciting reading.......2005-06-29

This is an excellent translation of an interesting Viking saga that has many parallels with Beowulf. The original author of this saga is unknown. It tells the story of King Hrolf Kraki's family and how he became king. There are also tales about his champions, their families and how they came to be in the service of Hrolf. This is one of the shorter sagas, only 77 pages, and reads easily. The story is filled with battles, sorcery, greed and deception. There is also an excellent introduction and notes section at the end of the book.

A MUST READ for any fan of medieval history........2003-02-06

Author, Jesse Byock, is considered the world's leading expert on the vikings. This new translation of the Norse epic brings clear a tale that is very similar to the story of Beowulf---however, it is told from the Norse point of view.

This is a MUST READ for anyone interested in the Vikings .

Interesting and Distinctive Saga.......2002-11-09

This is an interesting saga featuring semi-legendary Norse characters. It is presented and translated by the distinguished scholar of Icelandic history, Jesse Byock. The saga is a series of linked tales related to the life of the legendary Danish monarch, Hrolf Hraki. It is an example of a form of Icelandic saga based on the legendary or semi-legendary Norse past rather that the family or historical basis of many well known Icelandic sagas. This saga is drawn from the same stock of legends and characters used by the Beowulf poet. The stories are definitely interesting, the translation reads well, and Byock's introduction and notes are excellent. Nonetheless, this saga is of greater intellectual than artistic interest. Unlike Beowulf, this is a compilation of tales, not a unified poetic work. While the tales are good reading, this saga lacks the focus and poetic majesty of Beowulf. This saga lacks also the intensely realistic qualities of the family sagas and the unity derived from concentration on a few characters. This book is short, reads smoothly and is well worth the time expended on reading it.

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Saga of King Hrolf Kraki
Jesse Byock
Manufacturer: Penguin
ProductGroup: Book
Binding: Paperback
ASIN: B000K70DFA

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