Pseudo‐differential operators associated with Gyrator transform on Sobolev space
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DOI: 10.1002/mma.10585
Abstract: The main aim of this article is to focus on the fundamental properties of the gyrator transform on the Schwartz spaces. A more generalization Hörmander symbol class is introduced and studied the boundedness properties of… read more here.
Keywords: gyrator transform; pseudo differential; operators associated; differential operators ... See more keywords
Separability and Estimates for Eigenvalues and Singular Numbers of a Class of Hyperbolic‐Type Differential Operators
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DOI: 10.1002/mma.10829
Abstract: In this paper, we study the spectral properties of a class of differential operators of hyperbolic type with variable unbounded coefficients. We find conditions for the existence of a resolvent and maximum regularity of solutions.… read more here.
Keywords: hyperbolic type; estimates eigenvalues; separability estimates; class ... See more keywords
A Class of Pseudo‐Differential Operators Involving the Weinstein Transform
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DOI: 10.1002/mma.11163
Abstract: In this paper, the authors introduce and investigate a certain family of pseudo‐differential operators which is associated with the symbol class Sωr$$ {S}_{\omega}^r $$ on the space Sωℝ+n+1$$ {S}_{\omega}\left({\mathbb{R}}_{+}^{n+1}\right) $$ for a real‐valued convex function… read more here.
Keywords: weinstein transform; class; amp x0005e; differential ... See more keywords
First Order Differential Operators Associated to the Space of q-Monogenic Functions
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DOI: 10.1007/s00006-015-0583-4
Abstract: In this paper we characterize all the first order differential operators, with paravector coefficients, associated with the q-monogenic operator. Then initial value problems involving these operators are always solvable provided that the initial function is… read more here.
Keywords: differential operators; operators associated; first order; order differential ... See more keywords
Matrix Representation of Magnetic Pseudo-Differential Operators via Tight Gabor Frames
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DOI: 10.1007/s00041-024-10072-4
Abstract: In this paper we use some ideas from [12, 13] and consider the description of Hörmander type pseudo-differential operators on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^d$$\end{document} (d≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}… read more here.
Keywords: usepackage; magnetic pseudo; pseudo differential; differential operators ... See more keywords
Arithmetic differential operators on a semistable model of $${\mathbb {P}}^1$$P1
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DOI: 10.1007/s00209-018-2171-5
Abstract: In this paper we study sheaves of logarithmic arithmetic differential operators on a particular semistable model of the projective line. The main result here is that the first cohomology group of these sheaves contains a… read more here.
Keywords: semistable model; arithmetic differential; operators semistable; differential ... See more keywords
Conformally Covariant Bi-differential Operators for Differential Forms
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DOI: 10.1007/s00220-019-03431-6
Abstract: The classical Rankin–Cohen brackets are bi-differential operators from $$C^\infty ({\mathbb {R}})\times C^\infty ({\mathbb {R}})$$ C ∞ ( R ) × C ∞ ( R ) into $$ C^\infty ({\mathbb {R}})$$ C ∞ ( R )… read more here.
Keywords: infty mathbb; covariant differential; conformally covariant; differential forms ... See more keywords
$$L^{p}$$Lp-theory of elliptic differential operators with unbounded coefficients
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DOI: 10.1007/s00233-017-9855-8
Abstract: In this paper, we consider the generation of strongly continuous analytic semigroups on $$L^p((0,\omega ),\mu _{p}\, dx)$$Lp((0,ω),μpdx) and $$L^p((0,\omega ), dx), 1 read more here.
Keywords: theory elliptic; unbounded coefficients; differential operators; elliptic differential ... See more keywords
Hermitizable, isospectral complex matrices or differential operators
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DOI: 10.1007/s11464-018-0716-x
Abstract: The main purpose of the paper is looking for a larger class of matrices which have real spectrum. The first well-known class having this property is the symmetric one, then is the Hermite one. This… read more here.
Keywords: class; paper; isospectral complex; complex matrices ... See more keywords
Continuity of Gevrey–Hörmander pseudo-differential operators on modulation spaces
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DOI: 10.1007/s11868-018-0273-9
Abstract: Let $$s\ge 1$$s≥1, $$\omega ,\omega _0\in {\mathscr {P}}_{E,s}^0$$ω,ω0∈PE,s0, $$a\in \Gamma _{s}^{(\omega _0)}$$a∈Γs(ω0), and let $${\mathscr {B}}$$B be a suitable invariant quasi-Banach function space. Then we prove that the pseudo-differential operator $${\text {Op}}(a)$$Op(a) is continuous from… read more here.
Keywords: differential operators; omega mathscr; continuity gevrey; pseudo differential ... See more keywords
Strong Markov processes and negative definite functions associated with non-Archimedean elliptic pseudo-differential operators
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DOI: 10.1007/s11868-019-00293-3
Abstract: In this article we prove that the heat kernel attached to the non-Archimedean elliptic pseudodifferential operators determine a Feller semigroup and a uniformly stochastically continuous $$C_{0}$$ C 0 -transition function of some strong Markov processes… read more here.
Keywords: differential operators; markov processes; archimedean elliptic; strong markov ... See more keywords