Picone’s identity for biharmonic operators on Heisenberg group and its applications

Singular Convolution Operators on the Heisenberg Group

1. Statement of results and outline of method. The purpose of this note is to announce results dealing with convolution operators on the Heisenberg group. As opposed to the well-known situation where the kernels are homogeneous and C°° away from the origin, the kernels we study are homogeneous but have singularities on a hyperplane. Convolution operators with such kernels arise in the study of ...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

On a Picone's identity for the $mathcal{A}_{p(x)}$-Laplacian and its applications

‎We present a Picone's identity for the‎ ‎$mathcal{A}_{p(x)}$-Laplacian‎, ‎which is an extension of the classic‎ ‎identity for the ordinary Laplace‎. ‎Also‎, ‎some applications of our‎ ‎results in Sobolev spaces with variable exponent are suggested.

Picone’s Identity for the P-biharmonic Operator with Applications

In this article, a Picone-type identity for the weighted p-biharmonic operator is established and comparison results for a class of half-linear partial differential equations of fourth order based on this identity are derived.

On the Identity Problem for the Special Linear Group and the Heisenberg Group

We study the identity problem for matrices, i.e., whether the identity matrix is in a semigroup generated by a given set of generators. In particular we consider the identity problem for the Special Linear Group following recent NP-completeness result for SL(2,Z) and the undecidability for SL(4,Z) generated by 48 matrices. In the seminal paper of Paterson in 1970, an injective morphism from pai...