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Corpus ID: 119270403

On the absence of Volterra correct restrictions and extensions of the Laplace operator

@article{Biyarov2016OnTA,
title={On the absence of Volterra correct restrictions and extensions of the Laplace operator},
author={Bazarkan N. Biyarov},
journal={arXiv: Functional Analysis},
year={2016}
}

At the beginning of the last century J. Hadamard constructed the well-known example illustrating the incorrectness of the Cauchy problem for elliptic-type equations. If the Cauchy problem for some differential equation is correct, then it is usually a Volterra problem, i.e., the inverse operator is a Volterra operator. At present, not a single Volterra correct restriction or extension for elliptic-type equations is known. In the present paper, we prove the absence of Volterra correct… Expand

The study of the spectral properties of operators generated by differential equations of hyperbolic or parabolic type with Cauchy initial data involve, as a rule, Volterra boundary-value problems… Expand

I I . Min ima l d i f fe ren t i a l ope ra to r s w i t h c o n s t a n t coeff ic ients . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 N o t a t i o n s… Expand