Hilbert-type operator induced by radial weight

Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

On a Multiple Hilbert-Type Integral Operator and Applications

On Hilbert-type Integral Operator Inequality and Application

In the paper, by using the way of weight functions and the theory of operators, a Hilbert-type integral operator with the homogeneous kernel of −λ-degree and its norm are considered. As for applications, two equivalent inequalities with the best constant factors and some particular norms are obtained.

Approximation properties of certain operator-induced norms on Hilbert spaces

We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2. The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in a reproducing kernel Hilbert space (RKHS). Our results have implications to the analysi...