Some concrete operators and their properties


GÜRDAL M. , Garayev M. T. , SALTAN S.

TURKISH JOURNAL OF MATHEMATICS, cilt.39, ss.970-989, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 39 Konu: 6
  • Basım Tarihi: 2015
  • Doi Numarası: 10.3906/mat-1502-48
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.970-989

Özet

We consider integration and double integration operators, the Hardy operator, and multiplication and composition operators on Lebesgue space L-p [0,1] and Sobolev spaces W-p((n)) [0,1] and W-p((n)) ([0,1] x [0, 1]), and we study their properties. In particular, we calculate norm and spectral multiplicity of the Hardy operator and some multiplication operators, investigate its extended eigenvectors, characterize some composition operators in terms of the extended eigenvectors of the Hardy operator, and calculate the numerical radius of the integration operator on the real L-2 [0, 1] space. The main method for our investigation is the so-called Dulmmel products method. Some other questions are also discussed and posed.