TY  - JOUR
A1  - Mera, Azal Jaafar Musa
A1  - Tarkhanov, Nikolai
T1  - An elliptic equation of finite index in a domain
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - We give an example of first order elliptic equation for a complex-valued function in a plane domain which has a finite number of linearly independent solutions for any right-hand side. No boundary value conditions are thus required.
KW  - elliptic equation
KW  - Fredholm operator
KW  - index
Y1  - 2022
U6  - https://doi.org/10.1007/s40590-022-00442-7
SN  - 1405-213X
SN  - 2296-4495
VL  - 28
IS  - 2
PB  - Springer International
CY  - New York [u.a.]
ER  - 
TY  - JOUR
A1  - Chelkh, W.
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai
T1  - A remark on the Laplace transform
JF  - Siberian Mathematical Journal
N2  - The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.
KW  - Fourier-Laplace transform
KW  - distributions with one-sided support
KW  - holomorphic function
KW  - analytic functional
Y1  - 2020
U6  - https://doi.org/10.1134/S0037446620040151
SN  - 0037-4466
SN  - 1573-9260
VL  - 61
IS  - 4
SP  - 755
EP  - 762
PB  - Consultants Bureau, Springer
CY  - New York
ER  -