Magnetic Neumann Laplacian on a domain with hole

This article gives a domain with a small compact set of removed and the magnetic Neumann Laplacian on such set. The main theorem of this article shows the description of the holes which do not change the spectrum drastically. In this article we prove that the spectrum of the magnetic Neumann Laplacian converges in the Hausdorff distance sense to the spectrum of the original operator defined on the unperturbed domain

Designing a Mobile Device for Pre-hospital Care

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q-rational Functions and Interpolation with Complete Nevanlinna–Pick Kernels

In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels

Generalized qq-Fock spaces and structural identities

Using $q$-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their $q$-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative.Comment: References added to the q-Stirling number

Generalized q-Fock Spaces and Structural Identities

Using -calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their -calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative