ﻻ يوجد ملخص باللغة العربية
In this paper we prove Hormander-Mihlin multiplier theorems for pseudo-multipliers associated to the harmonic oscillator (also called the Hermite operator). Our approach can be extended to also obtain the $L^p$-boundedness results for multilinear pseudo-multipliers. By using the Littlewood-Paley theorem associated to the harmonic oscillator we also give $L^p$-boundedness and $L^p$-compactness properties for multipliers. $(L^p,L^q)$-estimates for spectral pseudo-multipliers also are investigated.
In this work we continue our research on nonharmonic analysis of boundary value problems as initiated in our recent paper (IMRN 2016). There, we assumed that the eigenfunctions of the model operator on which the construction is based do not have zero
We characterize the essential spectrum of the plasmonic problem for polyhedra in $mathbb{R}^3$. The description is particularly simple for convex polyhedra and permittivities $epsilon < - 1$. The plasmonic problem is interpreted as a spectral problem
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. First, we prove an analogue of the Paneah-Logvinenko-Sereda Theorem characterizing sets which satisfy the Geometric Control Condition (GCC). This resu
We study polynomial and exponential stability for $C_{0}$-semigroups using the recently developed theory of operator-valued $(L^{p},L^{q})$ Fourier multipliers. We characterize polynomial decay of orbits of a $C_{0}$-semigroup in terms of the $(L^{p}
The $(k,a)$-generalised Fourier transform is the unitary operator defined using the $a$-deformed Dunkl harmonic oscillator. The main aim of this paper is to prove $L^p$-$L^q$ boundedness of $(k, a)$-generalised Fourier multipliers. To show the boun