Nonharmonic analysis of boundary value problems
Michael Ruzhansky, Niyaz Tokmagambetov
TL;DR
This paper develops a global symbolic calculus for pseudo-differential operators associated with boundary value problems, including non-self-adjoint cases, and applies it to derive a-priori estimates for elliptic solutions.
Contribution
It introduces a non-self-adjoint distribution theory and biorthogonal Fourier analysis for boundary value problems, expanding the analytical tools available for non-elliptic operators.
Findings
Established a symbolic calculus for boundary value problems
Developed non-self-adjoint distribution theory
Derived a-priori estimates for elliptic solutions
Abstract
In this paper we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential operator. For this, we also establish elements of a non-self-adjoint distribution theory and the corresponding biorthogonal Fourier analysis. We give applications of the developed analysis to obtain a-priori estimates for solutions of operators that are elliptic within the constructed calculus.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Algebraic and Geometric Analysis · Mathematical Analysis and Transform Methods