Nonharmonic Analysis of Boundary Value Problems

By Michael Ruzhansky, Niyaz Tokmagambetov. 2015

92 citations recorded by the source corpus.

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. There are no assumptions on the regularity of the boundary which is allowed to have arbitrary singularities. We give applications of the developed analysis to obtain a priori estimates for solutions of boundary value problems that are elliptic within the constructed calculus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3ad9d10ccbc183e6caeffb2a5043807634469a5f

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In Applied Mathematics

1. J. Delgado
2. Niyaz Tokmagambetov
3. Michael Ruzhansky
4. Veronique Fischer
5. Ville T. Turunen

In Mathematical Physics

1. J. Delgado
2. Niyaz Tokmagambetov
3. Michael Ruzhansky
4. Veronique Fischer

Citations in the corpus

• Fourier multipliers, symbols, and nuclearity on compact manifolds (2014, background): “new data was collected or generated during the course of the research. 1 2 JULIODELGADOANDMICHAELRUZHANSKY We note that for some results, the self-adjointness and ellipticity of E can be dropped, see [RT15]. We give applications of these notions to the derivation of conditions characterising those i”
• Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary (2015, methodology): “In view of such further developments possible also in the present setting, we still prefer to use the term L-Fourier multiplier here, in line with [6] and [30].”