Semyon Yakubovich's Annual Report 2013

Semyon Yakubovich's Annual Report 2013

Year: 

2013

Brief description of the research activities: 

Área Analysis:

1. Kontorovich-Lebedev transform of polynomial sequences and central factorial numbers;

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

3. New classes of index transforms;

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

5. The iterated Stieltjes and Hilbert transforms.

Articles in international peer reviewed journals : 

The use of the Kontorovich-Lebedev transform in an analysis of regularized Schrödinger equation
The Kontorovich-Lebedev transform as a map between $d$-orthogonal polynomials
On some Rajchman measures and equivalent Salem's problem
On a heat kernel for the index Whittaker transform
Central factorials under the Kontorovich-Lebedev transform of polynomials
A Voronoi-type summation formula involving $\sigma_{\rm i\tau(n)$ and index transforms
A class of index transforms generated by the Mellin and Laplace operators
Another proof of Spira's inequality and its application to the Riemann hypothesis
A convolution operator related to the generalized Mehler-Fock and Kontorovich-Lebedev transforms
Operational calculus for the generalized fractional differential operator and applications
On the Yor integral and a system of polynomials related to the Kontorovich-Lebedev transform

Papers accepted for publication in peer reviewed journals: 

Semyon Yakubovich

Talks / Seminars / Courses : 

Student Mentoring: 

Sadegh Nazardonyavi, "A class of equivalent problems related to the Riemann hypothesis ", 2013

Editorial activities: 

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);

6. "The Pioneer Journal of Advances in Applied Mathematics" (India);

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