Complex Analysis and Special Topics in Harmonic Analysis
Published on 8. November 2011
Book
Paperback/Softback
X, 482 pages
978-1-4613-8447-2 (ISBN)
Description
A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.
More details
Edition
Softcover reprint of the original 1st ed. 1995
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
X, 482 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 27 mm
Weight
744 gr
ISBN-13
978-1-4613-8447-2 (9781461384472)
DOI
10.1007/978-1-4613-8445-8
Schweitzer Classification
Other editions
Additional editions
Carlos A. Berenstein | Roger Gay
Complex Analysis and Special Topics in Harmonic Analysis
Book
08/1995
Springer
€85.55
Article exhausted; check different version
Content
1 Boundary Values of Holomorphic Functions and Analytic Functionals.- 1.1. The Hardy Spaces in the Disk.- 1.2. Hyperfunctions.- 1.3. Analytic Functionals and Entire Functions of Exponential Type.- 1.4. Vade Mecum of Functional Analysis.- 1.5. Convolution of Analytic Functionals.- 1.6. Analytic Functionals on the Unit Circle.- 2 Interpolation and the Algebras Ap.- 2.1. The Algebras Ap.- 2.2. Interpolation with Growth Conditions.- 2.3. Ideal Theory in Ap.- 2.4. Dense Ideals in Ap(?).- 2.5. Local Ideals and Conductor Ideals in Ap.- 2.6. The Algebra A? of Entire Functions of Order at Most ?.- 3 Exponential Polynomials.- 3.1. The Ring of Exponential Polynomials.- 3.2. Distributions of Zeros of an Exponential Polynomial.- 4 Integral Valued Entire Functions.- 4.1. The G-Transform.- 4.2. Integral Valued Entire Functions.- 5 Summation Methods.- 5.1. Borel and Mittag-Leffler Summation Methods.- 5.2. The Lindelöf Indicator Function.- 5.3. The Fourier-Borel Transform of Order ? of Analytic Functionals.- 5.4. Analytic Functionals with Noncompact Carrier.- 6 Harmonic Analysis.- 6.1. Convolution Equations in ?.- 6.2. Convolution Equations in ?.- 6.3. The Equation f(z + 1) - f(z) = g(z).- 6.4. Differential Operators of Infinite Order.- 6.5. Deconvolution.- References.- Notation.