AN INVERSE PROBLEM FOR THE QUADRATIC PENCIL OF DIFFERENTIAL OPERATORS WITH ALMOST PERIODIC COEFFICIENTS

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Orujov A. D.

PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, cilt.48, sa.1, ss.3-19, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.30546/2409-4994.48.1.2022.3
  • Dergi Adı: PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.3-19
  • Anahtar Kelimeler: Almost periodic, Floquet solution, inverse problem, set of spectral data
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

In this paper, the inverse spectral problem for the operator L-lambda generated by the differential expression l(lambda)(y) = y'' + p(x)y' + lambda(2) + i lambda p(x) + q(x)] y is investigated in the space L-2(R). Here the coefficients p(x), q(x) are almost periodic functions whose Fourier series are absolutely convergent and the sequence of Fourier exponents (which arne positive) has a unique limit point at +infinity. The set of spectral data ({s(n)((1))}, {s(n)((2))})of the operator L-lambda is defined and the problem of finding the coefficients p(x), q(x) from these sequences is considered.