A new function-valued inner product and corresponding function-valued frames in L_2(0,∞)

摘要

In this paper for real number a > 1, we define a function-valued inner product on L_2(0,∞) by using dilation operator. We consider the relationship between orthonormal sequences, orthonormal bases and frames associated to the functionvalued inner product and orthonormal sequences, orthonormal bases and frames associated to the usual inner product in L_2(0,∞). Also the Bessel inequality and the relation between bounded linear operators on L_2(0,∞) associated to the function-valued inner product known function-valued factorable operators and frames respect to the function-valued inner product are discussed.