Some concrete operators and their properties

Authors : Mehmet Gürdal, Mubariz T. Garayev, Suna Saltan

Pages : 970-989

View : 13 | Download : 10

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :We consider integration and double integration operators, the Hardy operator, and multiplication and composition operators on Lebesgue space $L_{p}\left[ 0,1\right] $ and Sobolev spaces $W_{p}^{\left( n\right) }\left[ 0,1\right] $ and $W_{p}^{\left( n\right) }\left( \left[ 0,1\right] \times\left[ 0,1\right] \right) ,$ 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}\left[ 0,1\right] $ space. The main method for our investigation is the so-called Duhamel products method. Some other questions are also discussed and posed.
Keywords : Double integration operator, multiplication operator, composition operator, Sobolev space, Duhamel product, numerical radius