Harmonic Analysis and Boundary Value Problems in the Complex Domain

1. Front Matter

   Pages i-xiii

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2. Preliminary results. Integral transforms in the complex domain

   • Mkhitar M. Djrbashian

   Pages 1-22

3. Further results. Wiener-Paley type theorems

   • Mkhitar M. Djrbashian

   Pages 23-34

4. Some estimates in Banach spaces of analytic functions

   • Mkhitar M. Djrbashian

   Pages 35-59

5. Interpolation series expansions in spaces \( W_{1/2,\sigma }^{p,\omega } \) of entire functions

   • Mkhitar M. Djrbashian

   Pages 61-82

6. Fourier type basic systems in L₂(0, σ)

   • Mkhitar M. Djrbashian

   Pages 83-94

7. Interpolation series expansions in spaces \( W_{s + 1/2,\sigma }^{p,w} \) of entire functions

   • Mkhitar M. Djrbashian

   Pages 95-120

8. Basic Fourier type systems in L₂ spaces of odd-dimensional vector functions

   • Mkhitar M. Djrbashian

   Pages 121-140

9. Interpolation series expansions in spaces \( W_{s,\sigma }^{p,\omega }\) of entire functions

   • Mkhitar M. Djrbashian

   Pages 141-163

10. Basic Fourier type systems in L₂ spaces of even-dimensional vector functions

    • Mkhitar M. Djrbashian

    Pages 165-176

11. The simplest Cauchy type problems and the boundary value problems connected with them

    • Mkhitar M. Djrbashian

    Pages 177-210

12. Cauchy type problems and boundary value problems in the complex domain (the case of odd segments)

    • Mkhitar M. Djrbashian

    Pages 211-233

13. Cauchy type problems and boundary value problems in the complex domain (the case of even segments)

    • Mkhitar M. Djrbashian

    Pages 235-251

14. Back Matter

    Pages 253-258

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As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char­ acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan­ tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo­ nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com­ plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.

• Boundary value problem
• analytic function
• banach spaces
• boundary element method
• calculus
• differential equation
• distribution
• equation
• function
• functions
• harmonic analysis
• integral transform
• interpolation
• logical conclusion
• time

• Academy of Sciences of Armenia, Institute of Mathematics, Yerevan, Armenia

  Mkhitar M. Djrbashian

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