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Author: I_Uri_ Makarovich Berezanski_ Publisher: American Mathematical Soc. ISBN: 9780821898130 Category : Mathematics Languages : en Pages : 404
Book Description
Questions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses.
Author: I_Uri_ Makarovich Berezanski_ Publisher: American Mathematical Soc. ISBN: 9780821898130 Category : Mathematics Languages : en Pages : 404
Book Description
Questions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses.
Author: Vasyl Ostrovskyi Publisher: CRC Press ISBN: 9789058230423 Category : Mathematics Languages : en Pages : 272
Book Description
Provides the fundamentals of representations of finitely presented *-algebras by bounded operators. The theory is illustrated with numerous examples of *-algebra. The examples, in particular, include *-algebra with two self-adjoint generators that satisfy a quadratic or a more general relation, *-algebra with three or four generators, *-algebra that arise from one- and many-dimensional discrete dynamical systems. Wick *-algebra various; *-wild algebras. This book is intended for graduate students as well as researchers.
Author: Isao Miyadera Publisher: American Mathematical Soc. ISBN: 9780821886816 Category : Mathematics Languages : en Pages : 246
Book Description
This book presents a systematic exposition of the general theory of nonlinear contraction semigroups in Banach spaces and is aimed at students and researchers in science and engineering as well as in mathematics. Suitable for use as a textbook in graduate courses and seminars, this self-contained book is accessible to those with only a basic knowledge of functional analysis. After preprequisites presented in the first chapter, Miyadera covers the basic properties of dissipative operators and nonlinear contraction semigroups in Banach spaces. The generation of nonlinear contraction semigroups, the Komura theorem, and the Crandall-Liggett theorem are explored, and there is a treatment of the convergence of difference approximation of Cauchy problems for ????- dissipative operators and the Kobayashi generation theorem of nonlinear semigroups. Nonlinear Semigroups concludes with applications to nonlinear evolution equations and to first order quasilinear equations.
Author: Semen Grigorʹevich Gindikin Publisher: American Mathematical Soc. ISBN: 9780821897409 Category : Mathematics Languages : en Pages : 144
Book Description
This book is dedicated to two problems. The first concerns the description of maximal exponential growth of functions or distributions for which the Cauchy problem is well posed. The descriptions presented in the language of the behaviour of the symbol in a complex domain. The second problem concerns the structure of and explicit formulas for differential operators with large automorphism groups. It is suitable as an advanced graduate text in courses in partial differential equations and the theory of distributions.
Author: Eduard Prugovecki Publisher: Courier Corporation ISBN: 0486318052 Category : Science Languages : en Pages : 722
Book Description
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas. This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the gap between strictly physics- and mathematics-oriented texts on Hilbert space theory as applied to nonrelativistic quantum mechanics. Organized in the form of definitions, theorems, and proofs of theorems, it allows readers to immediately grasp the basic concepts and results. Exercises appear throughout the text, with hints and solutions at the end.
Author: S. A. Lomov Publisher: American Mathematical Soc. ISBN: 9780821897416 Category : Mathematics Languages : en Pages : 402
Book Description
This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.
Author: M. G. Goluzina Publisher: American Mathematical Soc. ISBN: 9780821897386 Category : Mathematics Languages : en Pages : 386
Book Description
This book is intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area. It differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. This book is unique in that the authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in mathematical folklore.
Author: Gennadij M. Fel'dman Publisher: American Mathematical Soc. ISBN: 9780821897447 Category : Mathematics Languages : en Pages : 236
Book Description
This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Author: Gennadiĭ Mikhaĭlovich Felʹdman Publisher: American Mathematical Soc. ISBN: 9780821845936 Category : Mathematics Languages : en Pages : 236
Book Description
This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Author: I_Uri_ Makarovich Berezanski_
Author: I_Uri_ Makarovich Berezanski_
Author: Israel Gohberg
Author: Vasyl Ostrovskyi
Author: Isao Miyadera
Author: Semen Grigorʹevich Gindikin
Author: Eduard Prugovecki
Author: S. A. Lomov
Author: M. G. Goluzina
Author: Gennadij M. Fel'dman
Author: Gennadiĭ Mikhaĭlovich Felʹdman