First Order Differential Operators Associated to the Space of q-Monogenic Functions
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Applied Clifford Algebras"
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
Arithmetic differential operators on a semistable model of $${\mathbb {P}}^1$$P1
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
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}$$ C 0 -transition function of some strong Markov processes… read more here.
Keywords: differential operators; markov processes; archimedean elliptic; strong markov ... See more keywords
Dixmier traces for discrete pseudo-differential operators
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DOI: 10.1007/s11868-020-00335-1
Abstract: In this paper we provide sharp results for the Dixmier traceability of discrete pseudo-differential operators on $$\ell ^2({\mathbb {Z}}^n)$$ ℓ 2 ( Z n ) . In this setting, we introduce a suitable notion of… read more here.
Keywords: differential operators; discrete pseudo; pseudo differential; dixmier traces ... See more keywords
Formal Factorization of Higher Order Irregular Linear Differential Operators
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DOI: 10.1007/s40598-019-00104-z
Abstract: We study the problem of formal decomposition (non-commutative factorization) of linear ordinary differential operators over the field $${{\mathbb {C}}}(\!(t)\!)$$C((t)) of formal Laurent series at an irregular singular point corresponding to $$t=0$$t=0. The solution (given in… read more here.
Keywords: formal factorization; factorization higher; order; factorization ... See more keywords
Differential operators on G/U and the Gelfand-Graev action
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DOI: 10.1016/j.aim.2022.108368
Abstract: Let G be a complex semisimple group and U its maximal unipotent subgroup. We study the algebra D(G/U) of algebraic differential operators on G/U and also its quasi-classical counterpart: the algebra of regular functions on… read more here.
Keywords: gelfand graev; differential operators; operators gelfand; graev action ... See more keywords
Cohomology of V ect(R) acting on the space of bilinear differential operators
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DOI: 10.1016/j.geomphys.2018.09.015
Abstract: Abstract We consider the V ect ( R ) -module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the vector fields… read more here.
Keywords: cohomology ect; differential operators; bilinear differential; ect acting ... See more keywords