Nonharmonic Analysis of Boundary Value Problems

  title={Nonharmonic Analysis of Boundary Value Problems},
  author={M. Ruzhansky and N. Tokmagambetov},
  journal={International Mathematics Research Notices},
  • M. Ruzhansky, N. Tokmagambetov
  • Published 2015
  • Mathematics
  • International Mathematics Research Notices
  • 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… CONTINUE READING


    Publications referenced by this paper.
    Elliptic Boundary Value Problems in Domains with Piecewise Smooth Boundary
    • 41
    Pseudo-differential operators generated by a non-local boundary value problem
    • 22
    Boundary value problems and layer potentials on manifolds with cylindrical ends
    • 25
    • PDF
    Mellin and Green symbols for boundary value problems on manifolds with edges
    • 16
    Discrete Fourier multipliers and cylindrical boundary-value problems
    • 6
    • Highly Influential
    • PDF
    The Asymptotic Distribution of Eigenvalues of Partial Differential Operators
    • 245
    Wave equation for sums of squares on compact Lie groups
    • 23
    • PDF
    Singular ordinary differential operators and pseudodifferential equations
    • 26
    Boundary problems for pseudo-differential operators
    • 449
    • Highly Influential
    • PDF
    Eigenfunction expansions of analytic functions
    • 29
    • PDF