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Function Theory in Polydiscs by Walter Rudin
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Function Theory in Polydiscs written by Walter Rudin
These notes with certain aspects of the theory of holomorphic fucntions of several complex variables which have not yet attracted much attention although they are very closely related to classical analysis. Briefly the object is to see how much of our extremly detailed knowledge about holomorphic fucntions in the unit disc (such as boundary values, distribution of zeros as related to growth restrictions, factorization theorems, invariant subspaces, interpolation theorems) can be carried over to an analogous situation in several variables, namely to polydiscs. It turns out that one finds some anlogues and many counter examples (as is to be expected) but also some genuinley new theorems whose one variable versions either make no sense or reduce to triviations. These differences are of course of much greater interest than similarities.
The notes are self contained, in the sense that anyone who is reasonably familiar with holomorphic functions of one variable, with measure and integrals, and with the rudiments of functional analysis should have no difficulty. All theorems are about several complex variables that are used are proved with one exception.
Book Detail :-
Title: Function Theory in Polydiscs
Author(s): Walter Rudin
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About Author :-
Author Walter Rudin (1921 – 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.
Rudin was known for his work on mathematical analysis, functional analysis, complex analysis and harmonic analysis. Rudin was also familiarly known to students as "Baby Rudin", "Papa Rudin", and "Grandpa Rudin"
He had obtain his Ph.D. from Duke University. He was a C. L. E. Moore Instructor at MIT. Principles, acclaimed for its elegance and clarity, has since become a standard textbook for introductory real analysis courses in the United States.
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• Download PDF Functional Analysis (2E) by Walter Rudin
• Download PDF Function Theory in Polydiscs by Walter Rudin
• Download PDF Function Theory in the Unit Ball of Cn by Walter Rudin
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Book Contents :-
Function Theory in Polydiscs written by Walter Rudin cover the following topics.
2. Poisson Integrals in Polydiscs
3. Hardy and Nevanlinna Spaces
4. Zero Set Problems
5. Inner Fucntions
6. Zeros and Interpolation on the Torus
7. Embeddings and Extensions
Symbols and Abbreviations
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