In previous work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants whose interest lay in the fact that quotients of them gave solutions to the cylindrical Toda equations. In the present paper we consider a more general class of operators which retain some of the properties of those cited and we find analogous asymptotics for the determinants.

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...

This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients {〈k,Φm,n〉} of certain frame expansions of the kernel k of an integral operator are in l, then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a parti...

It is well known that the signature operator on a manifold defines a K-homology class which is an orientation after inverting 2. Here we address the following puzzle: what is this class localized at 2, and what special properties does it have? Our answers include the following: • the K-homology class ∆M of the signature operator is a bordism invariant; • the reduction mod 8 of the K-homology cl...

Motivated by Carlson-Shaffer linear operator, we define here a new generalized linear operator. Using this operator, we define a class of analytic functions in the unit disk U. For this class, a majorization problem of analytic functions is discussed.

The question whether every operator on H has an hyperinvariant subspace is one of the most difficult problems in operator theory. The purpose of this paper is to make a beginning on the hyperinvariant subspace problems for another class of operators closely related to the normal operators namely, the class of k -quasi-class A operators. A necessary and sufficient condition for the hypercyclicit...