$p$-Hyperbolic Zolotarev Functions in Boundary Value Problems for a $p\,$th order Differential Operator
Functional Analysis
2023-02-06 v1
Abstract
For the self-adjoint operator of the th derivative, a system of fundamental solutions is constructed. This system is analogues to the classical system of sines and cosines. The properties of such functions are studied. Classes of self-adjoint boundary conditions are described. For the operator of the third derivative, the resolvent is calculated and an orthonormal basis of eigenfunctions is given.
Cite
@article{arxiv.2302.01573,
title = {$p$-Hyperbolic Zolotarev Functions in Boundary Value Problems for a $p\,$th order Differential Operator},
author = {M. F. Bessmertny\uı and V. A. Zolotarev},
journal= {arXiv preprint arXiv:2302.01573},
year = {2023}
}