Dimitar Kolev Dimitrov

• Abstract

  The principal themes of the present project are Harmonic Analysis and Analytic Number Theory. We shall study various general topics related to Classical Analysis and the Theory of Entire Functions as well as problems about correlations of zeros of the Riemann zeta function. (AU)

  Topics in analysis and analytic number theory, AV.EXT

• Abstract

  The principal topics of the present project are the Heine-Stieltjes theory concerning the Lamé differential equations and its applications to electrostatics. Problems about analysis of Lamé's equation, as well as questions about the existence and uniqueness of an equilibrium of electrostatics fields of a rather involved nature that obey the law of the logarithmic potential will be studie…

  Heine-Stieltjes theory and electrostatics, AV.EXT

• Abstract

  The principal objectives of this project are to study themes related to Harmonic Analysis, Approximation Theory and Special Functions and their Applications. Harmonic Analysis is a cornerstone of Analysis. The solutions of the principal partial differential equation are generally represented by convolutions and these representations are obtained via an application of the Fourier transform…

  Harmonic analysis, approximation theory and applications, AP.TEM

(Only some records are available in English at this moment)

• Abstract

  The principal aim of this project is to study conditions for an entire function defined as a Fourier transform of a positive kernel to possess only real zeros. A special case inspired naturally by the properties of the Riemann xi-function is when the kernel is related to a modular or a quasi-modular form.

  The Laguerre-Pólya class theory of functions and applications in the Analytic Number Theory, BP.PD

• Abstract

  Among the efficient tools to study the distribution of the prime numbers, which is a principal theme in Number Theory, are the so-called Vinogradov-Korobov method and also the analysis of the entire functions, represented in terms of a Fourier transform, whose zeros are all real. Both tools have their origin in Harmonic Analysis. Other applications which reveal the fundamental role of thi…

  Harmonic analysis and Number Theory, BP.DR

• Abstract

  This project aims the study of asymptotic behavior of orthogonal polynomials, via Riemann-Hilbert approach, and the study of the relations between these polynomials and another fields of mathematics like random matrices theory.

  Orthogonal Polynomials and Random Matrices: Study and Characterization via Riemann-Hilbert Problem, BP.MS

(Only some records are available in English at this moment)

• Abstract

  The principal objectives of the present research project is to continue our collaboration with colleagues from Sofia University, with whom we have maintained permanent contact along the years and have produced some interesting joint results. The principal themes that we shall approach are: Inequalities from Approximation Theory and Harmonic Analysis such as Markov's, Bernstein's and Hardy…

  Topic in classical analysis and approximation theory, BE.PQ