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A Complex Analysis Problem Book (Repost)

Posted By: AvaxGenius
A Complex Analysis Problem Book (Repost)

A Complex Analysis Problem Book by Daniel Alpay
English | PDF | 2011 | 526 Pages | ISBN : 3034800770 | 4.6 MB

This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises show the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.

Complex Analysis with Applications to Number Theory

Posted By: AvaxGenius
Complex Analysis with Applications to Number Theory

Complex Analysis with Applications to Number Theory by Tarlok Nath Shorey
English | EPUB | 2020 | 297 Pages | ISBN : 9811590966 | 23.8 MB

The book discusses major topics in complex analysis with applications to number theory. This book is intended as a text for graduate students of mathematics, undergraduate students of engineering and researchers in fields of complex analysis and number theory. This theory is a prerequisite for the study of various areas of mathematics, including the theory of several finitely and infinitely complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. In addition to solved examples and problems, the book covers most topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, Gamma function, and harmonic functions.

Potential Theory on Sierpiński Carpets: With Applications to Uniformization

Posted By: AvaxGenius
Potential Theory on Sierpiński Carpets: With Applications to Uniformization

Potential Theory on Sierpiński Carpets: With Applications to Uniformization by Dimitrios Ntalampekos
English | PDF,EPUB | 2020 | 192 Pages | ISBN : 3030508048 | 16 MB

This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpiński carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces.