ON THE SOLVABILITY OF SOME OPERATOR EQUATIONS

Tapdigoglu R., Garayev M.

REAL ANALYSIS EXCHANGE, vol.49, no.1, pp.189-204, 2024 (ESCI) identifier identifier

  • Nəşrin Növü: Article / Article
  • Cild: 49 Say: 1
  • Nəşr tarixi: 2024
  • Doi nömrəsi: 10.14321/realanalexch.49.1.1694401973
  • jurnalın adı: REAL ANALYSIS EXCHANGE
  • Jurnalın baxıldığı indekslər: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, Public Affairs Index, zbMATH, DIALNET
  • Səhifə sayı: pp.189-204
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

We consider the Volterra integration operator V, V f(x) = integral(x)(0) f(t) dt, on the following subspace of the Wiener algebra W[0, 1]: W-(1)[0, 1] := {f is an element of W[0, 1] : f' is an element of W[0, 1]}. We investigate solvability of the operator equations VA = lambda AV and VA = lambda A(2)V, where lambda is an element of C is a complex number. Our proof is based on the Duhamel product of functions defined by (f circle star g)(x) := d/dx integral(x)(0) f(x - t) g(t) dt.