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Generalized Functions. Volume I: Properties and Operations (English and Russian Edition)

Science & Math

G. E. Shilov

I. M. Gel'fand

Mathematics

Academic Press

Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions

Israel M. Gel'fand

Generalized Functions, Vol. 3: Theory of Differential Equations

Academic Press Inc.,U.S.

This graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and useful alternative to customary approaches. The treatment can be understood by any reader with a solid background in advanced calculus, and it features many problems with hints and answers. "The exposition is fresh and sophisticated," declared Sci-Tech Book News, "and will engage the interest of accomplished mathematicians." Part one is devoted to the integral, moving from the Reimann integral and step functions to a general theory, and obtaining the "classical" Lebesgue integral in n space. Part two constructs the Lebesgue-Stieltjes integral through the Daniell scheme using the Reimann-Stieltjes integral as the elementary integral. Part three develops theory of measure with the general Daniell scheme, and the final part is devoted to the theory of the derivative.

Integral, Measure and Derivative: A Unified Approach (Dover Books on Mathematics)

B. L. Gurevich

Dover Publications

The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.

Generalized Functions: Properties and Operations (AMS Chelsea Publishing)

I.M. Gelfand

American Mathematical Society

The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel'fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countable-normed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley-Wiener theorem.

The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. In Volume 3, applications of generalized functions to the Cauchy problem for systems of partial differential equations with constant coefficients are considered. The book includes the study of uniqueness classes of solutions of the Cauchy problem and the study of classes of functions where the Cauchy problem is well posed. The last chapter of this volume presents results related to spectral decomposition of differential operators related to generalized eigenfunctions.

Generalized Functions, Volume 3: Theory of Differential Equations (Ams Chelsea Publishing, 379)

See the best price to sell, buy, or rent books by G. E. Shilov. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by G. E. Shilov

See the best price to sell, buy, or rent books by G. E. Shilov. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Generalized Functions. Volume I: Properties and Operations (English and Russian Edition)

Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions

Generalized Functions, Vol. 3: Theory of Differential Equations

Integral, Measure and Derivative: A Unified Approach (Dover Books on Mathematics)

Generalized Functions: Properties and Operations (AMS Chelsea Publishing)

Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions

Generalized Functions, Volume 3: Theory of Differential Equations (Ams Chelsea Publishing, 379)