An inverse problem for weighted PaleyWiener spaces
Abstract
Let μ be a measure on the real line {{R}} such that {\int }_{{{R}}}\tfrac{{{d}}μ (t)}{1+{t}^{2}}\lt ∞ and let a\gt 0. Assume that the norms \parallel f{\parallel }_{{L}^{2}({{R}})} and \parallel f{\parallel }_{{L}^{2}(μ )} are comparable for functions f in the PaleyWiener space {{PW}}_{a} and that {{PW}}_{a} is dense in {L}^{2}(μ ). We reconstruct the canonical Hamiltonian system {JX}^{\prime} =z{ H }X such that μ is the spectral measure for this system.
The work is supported by Russian Science Foundation Grant 142100035 (theorem 1) and by Russian Science Foundation Grant 144100010 (theorem 2).
 Publication:

Inverse Problems
 Pub Date:
 November 2016
 DOI:
 10.1088/02665611/32/11/115007
 arXiv:
 arXiv:1509.08117
 Bibcode:
 2016InvPr..32k5007B
 Keywords:

 Mathematical Physics;
 Mathematics  Functional Analysis;
 Primary 34L05;
 Secondary 47B35
 EPrint:
 14 pages