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1.
《Journal of Pure and Applied Algebra》2022,226(10):107043
We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labelled by an arbitrary finite-dimensional representation. As a special case, we obtain a categorification of the coloured Jones polynomial of links. 相似文献
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《Mathematische Nachrichten》2018,291(8-9):1177-1190
We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings. 相似文献
5.
We prove a sharp estimate for the k-modulus of smoothness, modelled upon a -Lebesgue space, of a function f in , where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, , and . This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings. 相似文献
6.
In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process , for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes. 相似文献
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Jamil Chaker 《Mathematische Nachrichten》2019,292(11):2316-2337
We consider systems of stochastic differential equations of the form for with continuous, bounded and non‐degenerate coefficients. Here are independent one‐dimensional stable processes with . In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices. 相似文献
9.
Shai Shechter 《Journal of Pure and Applied Algebra》2019,223(10):4384-4425
Let be a complete discrete valuation ring with finite residue field of odd characteristic, and let G be a symplectic or special orthogonal group scheme over . For any let denote the ?-th principal congruence subgroup of . An irreducible character of the group is said to be regular if it is trivial on a subgroup for some ?, and if its restriction to consists of characters of minimal -stabilizer dimension. In the present paper we consider the regular characters of such classical groups over , and construct and enumerate all regular characters of , when the characteristic of is greater than two. As a result, we compute the regular part of their representation zeta function. 相似文献
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