Sökning: "Paley-Wiener theorem"

Hittade 2 avhandlingar innehållade orden Paley-Wiener theorem.

  1. 1. Titchmarsh-Weyl M-function asymptotics and some results in the inverse spectral theory for vector-valued Sturm-Liouville equations and a certain higher order ordinary differential equation

    Författare :Erik Andersson; Matematik (naturvetenskapliga fakulteten); []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Functions; differential equations; Funktioner; differentialekvationer; Paley-Wiener.; The generalized Fourier transform; A certain higher order ordinary differential equation; Borg-Marchenko theorems; Vector-valued Sturm-Liouville equations; Inverse spectral theory; Titchmarsh-Weyl M-function asymptotics; Asymptotics of solutions; Spectral measure;

    Sammanfattning : This discourse is constituted by two separate reprots, where the first one offers an elementary deduction of the leading order term asymptotics for the Titchmarsh-Weyl M-function corresponding to a vector-valued Sturm-Liouville equation of the form -(PU')'+QU=zu, xin[0,b), with P^{-1},W,Q being hermitean with locally integrable entries; and under some additional conditions on P^{-1} and W. In the special case of P=W=I, we give some further asymptotic results for the same M-function. LÄS MER

  3. 2. Infinite dimensional holomorphy in the ring of formal power series : partial differential operators

    Författare :Henrik Petersson; Andrei Khrennikov; Sean Dineen; Växjö universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Infinite dimensional holomorphy; Formal power series; Fourier-Borel transform; Paley-Wiener theorem; Fischer decomposition; Fischer pair; Fock space; Cauchy-Problem; Kergin operator; PDE-preserving; Pseudo-differential operators.; MATHEMATICS; MATEMATIK;

    Sammanfattning : We study holomorphy in the ring of formal power series in an infinite number of variables. Thus we restrict our study to (infinite dimensional) holomorphy on sequence spaces and we show that we obtain a rich theory without requiring any topological structure on the domain space. We make a comprehensive PDO-study for the spaces under consideration. LÄS MER