Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions (Ams Chelsea Publishing)

I. M. Gelfand, G. E. Shilov

ISBN 10: 1470426595 / ISBN 13: 9781470426590

Verlag: American Mathematical Society, 2016

Beschreibung

New.

Bestandsnummer des Verkäufers D8S0-3-M-1470426595-6

Bibliografische Details

• Titel: Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions (Ams Chelsea Publishing)
• Verlag: American Mathematical Society
• Veröffentlichungsdatum: 2016
• Sprache: Englisch
• ISBN-10: 1470426595
• ISBN-13: 9781470426590
• Bindung: Hardcover
• Zustand: New
• Buchtyp: book

Über diesen Titel

Inhaltsangabe

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 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.

Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.