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Catalogue Information
Field name	Details
Dewey Class	515
Title	Complex Analysis and Special Topics in Harmonic Analysis ([EBook] /) / by Carlos A. Berenstein, Roger Gay.
Author	Berenstein, Carlos A.
Added Personal Name	Gay, Roger author.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York, , 1995.
Physical Details	X, 482 p. : online resource.
ISBN	9781461384458
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4613-8445-8
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Lie groups . Mathematical analysis . Mathematics . Topological groups . Topological groups, Lie groups . Authors: Berenstein, Carlos A. . Gay, Roger . Corporate Authors: SpringerLink (Online service) . Classification: 515 .

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Complex Analysis and Special Topics in Harmonic Analysis

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