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Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 146125700X
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehen sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have non trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatter ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools.
Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 146125700X
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehen sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have non trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatter ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools.
Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 3662126788
Category : Mathematics
Languages : en
Pages : 610
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Book Description
Author: Tosio Kato
Publisher: Springer
ISBN: 9780387586618
Category : Linear operators.
Languages : en
Pages : 619
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Book Description
Author:
Publisher:
ISBN:
Category : Linear operators
Languages : en
Pages : 619
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Book Description
Author: Oscar Gonzalez
Publisher: American Mathematical Society
ISBN: 147046991X
Category : Mathematics
Languages : en
Pages : 228
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Book Description
The analysis and interpretation of mathematical models is an essential part of the modern scientific process. Topics in Applied Mathematics and Modeling is designed for a one-semester course in this area aimed at a wide undergraduate audience in the mathematical sciences. The prerequisite for access is exposure to the central ideas of linear algebra and ordinary differential equations. The subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have some experience. Students who use this book will enhance their understanding of mathematics, acquire tools to explore meaningful scientific problems, and increase their preparedness for future research and advanced studies. The highlights of the book are case studies and mini-projects, which illustrate the mathematics in action. The book also contains a wealth of examples, figures, and regular exercises to support teaching and learning. The book includes opportunities for computer-aided explorations, and each chapter contains a bibliography with references covering further details of the material.
Author: Wolfgang Arendt
Publisher: Springer Science & Business Media
ISBN: 3034850751
Category : Mathematics
Languages : en
Pages : 526
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Book Description
Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .
Author: Yuji Aruka
Publisher: Springer Science & Business Media
ISBN: 3790826189
Category : Business & Economics
Languages : en
Pages : 278
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Book Description
As the real world is rapidly becoming more and more complicated, economists need to venture beyond the boundaries of mainstream economics and integrate philosophical thought and complexity into their analytical frameworks. In this context, this volume brings together papers on economic theory and its related issues, exploring complex production systems and heterogeneously interacting human behavior. The author challenges economists to integrate economic theory and moral science anew by referring to evolutionary economics and socio-econophysics. The three parts of the book focus on the complexities of production and social interaction, the moral science of heterogeneous economic interaction, and the Avatamsaka’s dilemma of the two-person game with only positive spillovers.
Author: Ernst Eberlein
Publisher: Birkhäuser
ISBN: 3034888295
Category : Mathematics
Languages : en
Pages : 336
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Book Description
What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.
Author: Francoise Chatelin
Publisher: SIAM
ISBN: 0898719992
Category : Mathematics
Languages : en
Pages : 482
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Book Description
Originally published: New York: Academic Press, 1983.
Author: Rajendra Bhatia
Publisher: SIAM
ISBN: 0898716314
Category : Mathematics
Languages : en
Pages : 200
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Book Description
For the SIAM Classics edition, the author has added over 60 pages of material covering recent results and discussing the important advances made in the last two decades. It is an excellent research reference for all those interested in operator theory, linear algebra, and numerical analysis.
