Author | Berenstein, Carlos A. author |
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Title | Complex Analysis and Special Topics in Harmonic Analysis [electronic resource] / by Carlos A. Berenstein, Roger Gay |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8445-8 |
Descript | X, 482 p. online resource |
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 MittagโLeffler Summation Methods -- 5.2. The Lindelรถf Indicator Function -- 5.3. The FourierโBorel 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) โ f(z) = g(z) -- 6.4. Differential Operators of Infinite Order -- 6.5. Deconvolution -- References -- Notation