Complex Analysis and Special Topics in Harmonic Analysis

1. Front Matter

   Pages i-x

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2. Boundary Values of Holomorphic Functions and Analytic Functionals

   • Carlos A. Berenstein, Roger Gay

   Pages 1-108

3. Interpolation and the Algebras AP

   • Carlos A. Berenstein, Roger Gay

   Pages 109-197

4. Exponential Polynomials

   • Carlos A. Berenstein, Roger Gay

   Pages 198-259

5. Integral Valued Entire Functions

   • Carlos A. Berenstein, Roger Gay

   Pages 260-298

6. Summation Methods

   • Carlos A. Berenstein, Roger Gay

   Pages 299-352

7. Harmonic Analysis

   • Carlos A. Berenstein, Roger Gay

   Pages 353-469

8. Back Matter

   Pages 471-482

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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.

• Complex analysis
• calculus
• differential equation
• functional analysis
• harmonic analysis

• Mathematics Department and Institute for Systems Research, University of Maryland, College Park, USA

  Carlos A. Berenstein

• Centre de Recherche en Mathématiques, Université de Bordeaux I, Talence (cedex), France

  Roger Gay