Carleman's formula for the generalized Cauchy-Riemann system

Carleman's formula for the generalized Cauchy-Riemann system

Authors

  • Ermamatova Fotima E.,
  • Ermamatova Bibixojar E.

Abstract

Using results from [2], [3], [4] on solving the Cauchy problem, we construct the Carleman matrix
for the Laplace and Helmholts equations in explicit form and, on its basis, the regularized solution of the
Cauchy problem for system (1). By using the continuation formula we found necessary and sufficient for
the extendibility of functions given an a part of a boundary to the domain as a solution of the system (1).
We prove the Fock-Kyni theorem fore this one. 

References

Obolashvili E. I. ―The spatial analog of generalized analytic functions, ‖Soobshch. AN GSSR 73(1), 20–24 (1974).

Lavrent‘ev M.M. Some Ill-Posed Problems of Mathematical Physics, Novosib., 1962, 92 pp.

Yarmukhamedov Sh. // Dokl. Akad.Nauk SSSR, 235(2), 281-283(1977).

Yarmukhamedov Sh. // Dokl. Ross. Akad.Nauk 357(3), 320-323 (1997)

Published

2024-06-06

How to Cite

Ermamatova, F. E., & Ermamatova, B. E. (2024). Carleman’s formula for the generalized Cauchy-Riemann system : Carleman’s formula for the generalized Cauchy-Riemann system . MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS, 1(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/637

Issue

Vol. 1 No. 01 (2024): INTERNATIONAL CONFERENCE

Section

Mathematical analysis, differential equations and equations of mathematical physics