Semyon Yakubovich's Annual Report 2014

Semyon Yakubovich's Annual Report 2014

Year: 

2014

Brief description of the research activities: 

Área Analysis:

1. Equivalences to the Riemann hypothesis and properties of the Riemann zeta-function;

2. New classes of index transforms;

3. Towards solution to the Casas-Alvero conjecture. Properties of Goncharov's polynomials.

4. The iterated Stieltjes and Hilbert transforms

5. The iterated half- Hartley transform

6. New identities for Bernoulli, Euler numbers and Riemann zeta values at integers.

7. Salem's type equivalences to the Riemann hypothesis revisited

8. Eigenfunctions of Fourier operators and the KL-transform

9. Borel type expansions and the KL-transform.

Articles in international peer reviewed journals : 

Time-dependent problems for a wedge via Kontorovich-Lebedev's transform
The Plancherel, Titchmarsh and convolution theorems for the half-Hartley transform
On the iterated Stieltjes transform and its convolution with applications to singular integral equations
New inversion, convolution and Titchmarsh's theorems for the half-Hilbert transform
Integral and series transformations via Ramanujan's identities and Salem's type equivalences to the Riemann hypothesis
On a polynomial sequence associated with the Bessel operator

Papers accepted for publication in peer reviewed journals: 

Semyon Yakubovich

Talks / Seminars / Courses : 

Editorial activities: 

Member of the Editorial Board of International Journals:

1. "Hacettepe Journal of Mathematics and Statistics" (Turkey);

2. "Thai Journal of Mathematics" (Tailand);

3. "Opuscula Mathematica" (Poland);

4. "Sarajevo Journal of Mathematics" (Bosnia e Herzegovina);

5. "Integral Transforms and Special Functions" (UK) (associate editor);

Work visits: 

AGH University of Krakow, Poland. May 4-8, 2014.

Reports: 

Title of the talk on seminar on "Functional Analysis and Applications": The half-Hilbert, half-Hartley transforms: convolution and Titchmarsh's theorems and applications to singular integral equations". Department of Mathematics, May 7, 2014.