Author | Djrbashian, Mkhitar M. author |
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Title | Harmonic Analysis and Boundary Value Problems in the Complex Domain [electronic resource] / by Mkhitar M. Djrbashian |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1993 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8549-2 |
Descript | XIII, 258 p. online resource |
1 Preliminary results. Integral transforms in the complex domain -- 1.1 Introduction -- 1.2 Some identities -- 1.3 Integral representations and asymptotic formulas -- 1.4 Distribution of zeros -- 1.5 Identities between some Mellin transforms -- 1.6 Fourier type transforms with Mittag-Leffler kernels -- 1.7 Some consequences -- 1.8 Notes -- 2 Further results. Wiener-Paley type theorems -- 2.1 Introduction -- 2.2 Some simple generalizations of the first fundamental Wiener-Paley theorem -- 2.3 A general Wiener-Paley type theorem and some particular results -- 2.4 Two important cases of the general Wiener-Paley type theorem -- 2.5 Generalizations of the second fundamental Wiener-Paley theorem -- 2.6 Notes -- 3 Some estimates in Banach spaces of analytic functions -- 3.1 Introduction -- 3.2 Some estimates in Hardy classes over a half-plane -- 3.3 Some estimates in weighted Hardy classes over a half-plane -- 3.4 Some estimates in Banach spaces of entire functions of exponential type -- 3.5 Notes -- 4 Interpolation series expansions in spacesW1/2,?p,?of entire functions -- 4.1 Introduction -- 4.2 Lemmas on special Mittag-Leffler type functions -- 4.3 Two special interpolation series -- 4.4 Interpolation series expansions -- 4.5 Notes -- 5 Fourier type basic systems inL2(0, ?) -- 5.1 Introduction -- 5.2 Biorthogonal systems of Mittag-Leffler type functions and their completeness inL2(0, ?) -- 5.3 Fourier series type biorthogonal expansions inL2(0, ?) -- 5.4 Notes -- 6 Interpolation series expansions in spacesWs+1/2,?p,?of entire functions -- 6.1 Introduction -- 6.2 The formulation of the main theorems -- 6.3 Auxiliary relations and lemmas -- 6.4 Further auxiliary results -- 6.5 Proofs of the main theorems -- 6.6 Notes -- 7 Basic Fourier type systems inL2spaces of odd-dimensional vector functions -- 7.1 Introduction -- 7.2 Some identities -- 7.3 Biorthogonal systems of odd-dimensional vector functions -- 7.4 Theorems on completeness and basis property -- 7.5 Notes -- 8 Interpolation series expansions in spacesWs,?p,?of entire functions -- 8.1 Introduction -- 8.2 The formulation of the main interpolation theorem -- 8.3 Auxiliary relations and lemmas -- 8.4 Further auxiliary results -- 8.5 The proof of the main interpolation theorem -- 8.6 Notes -- 9 Basic Fourier type systems inL2spaces of even-dimensional vector functions -- 9.1 Introduction -- 9.2 Some identities -- 9.3 The construction of biorthogonal systems of even-dimensional vector functions -- 9.4 Theorems on completeness and basis property -- 9.5 Notes -- 10 The simplest Cauchy type problems and the boundary value problems connected with them -- 10.1 Introduction -- 10.2 Riemann-Liouville fractional integrals and derivatives -- 10.3 A Cauchy type problem -- 10.4 The associated Cauchy type problem and the analog of Lagrange formula -- 10.5 Boundary value problems and eigenfunction expansions -- 10.6 Notes -- 11 Cauchy type problems and boundary value problems in the complex domain (the case of odd segments) -- 11.1 Introduction -- 11.2 Preliminaries -- 11.3 Cauchy type problems and boundary value problems containing the operators $$ {\mathbb{L}_{s + 1/2}}$$ and $$ \mathbb{L}_{s + 1/2}̂*$$ -- 11.4 Expansions inL2{?2s+1(?)} in terms of Riesz bases -- 11.5 Notes -- 12 Cauchy type problems and boundary value problems in the complex domain (the case of even segments) -- 12.1 Introduction -- 12.2 Preliminaries -- 12.3 Cauchy type problems and boundary value problems containing the operators $${{\mathbb{L}}_{s}} $$ and $$ \mathbb{L}_{s}̂*$$ -- 12.4 Expansions inL2{?2s(?)} in terms of Riesz bases -- 12.5 Notes