In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussian , we will construct an uncountable family of lattices [Formula: see text] such that each pairing of with some [Formula: see text] yields a Gabor frame, and all pairings yield the same frame bounds. On the other hand, for each lattice we will find a countable family of generalized Gaussians [Formula: see text] such that each pairing leaves the frame bounds invariant. Therefore, we are tempted to speak about .

In this article, we introduce a generalized -Laplace transform and discuss some essential results of integral transform theory, in particular, involving a -Hilfer pseudo-fractional derivative and function convolution. In this sense, we investigated the existence and uniqueness of known solutions for a pseudo-fractional differential equation.

We present a construction of algebras of generalized functions of Colombeau-type which, instead of asymptotic estimates with respect to a regularization parameter, employs only topological estimates on certain spaces of kernels for its definition.

The purpose of this article is to study new non-Archimedean pseudo-differential operators whose symbols are determined from the behavior of two functions defined on the -adic numbers. Thanks to the characteristics of our symbols, we can find connections between these operators and new types of non-homogeneous differential equations, Feller semigroups, contraction semigroups and strong Markov processes.