共查询到20条相似文献,搜索用时 31 毫秒
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Aingeru Fernández-Bertolin Karlheinz Gröchenig Philippe Jaming 《Journal of Mathematical Analysis and Applications》2019,469(1):202-219
The aim of this paper is to establish uniqueness properties of solutions of the Helmholtz and Laplace equations. In particular, we show that if two solutions of such equations on a domain of agree on two intersecting -dimensional submanifolds in generic position, then they agree everywhere. 相似文献
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《Indagationes Mathematicae》2023,34(3):643-659
We give an asymptotic formula for the number of sublattices of index at most for which has rank at most , answering a question of Nguyen and Shparlinski. We compare this result to work of Stanley and Wang on Smith normal forms of random integral matrices and discuss connections to the Cohen–Lenstra heuristics. Our arguments are based on Petrogradsky’s formulas for the cotype zeta function of , a multivariable generalization of the subgroup growth zeta function of . 相似文献
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Hao Sun 《Discrete Mathematics》2019,342(3):715-722
-operators are differential operators on the polynomial ring. Mironov, Morosov and Natanzon construct the generalized Hurwitz numbers. They use the -operator to prove a formula for the generating function of the generalized Hurwitz numbers. A special example of the -operator is the cut-and-join operator. Goulden and Jackson use the cut-and-join operator to calculate the simple Hurwitz number. In this paper, we study the relation between -operator and the central elements in . Based on the relation we find, we give another proof about a differential equation of the generating function of -Hurwitz number. 相似文献
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Eduardo Abi Jaber Bruno Bouchard Camille Illand 《Stochastic Processes and their Applications》2019,129(5):1726-1748
This paper provides a new characterization of the stochastic invariance of a closed subset of with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable: we only assume that the covariance matrix is. In particular, our result can be applied to construct affine and polynomial diffusions on any arbitrary closed set. 相似文献
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Luigi Ambrosio Shouhei Honda Jacobus W. Portegies David Tewodrose 《Journal of Functional Analysis》2021,280(10):108968
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results [10], [11] known for closed Riemannian manifolds, we prove convergence as of the rescaled pull-back metrics in induced by . Moreover we discuss the behavior of with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative -convergence in the noncollapsed setting for all , a result new even for closed Riemannian manifolds and Alexandrov spaces. 相似文献
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Jinghai Shao 《Stochastic Processes and their Applications》2019,129(1):153-173
In this work we prove the existence and uniqueness of the optimal transport map for -Wasserstein distance with , and particularly present an explicit expression of the optimal transport map for the case . As an application, we show the existence of geodesics connecting probability measures satisfying suitable condition on path groups and loop groups. 相似文献
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《Discrete Mathematics》2020,343(9):111949
A well known theorem in graph theory states that every graph on vertices and minimum degree at least contains a path of length at least , and if is connected and then contains a path of length at least (Dirac, 1952). In this article, we give an extension of Dirac’s result to hypergraphs. We determine asymptotic lower bounds of the minimum degrees of 3-graphs to guarantee linear paths of specific lengths, and the lower bounds are tight up to an error term depending only on the lengths of the paths. 相似文献
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Alex Iosevich Chun-Kit Lai Azita Mayeli 《Applied and Computational Harmonic Analysis》2019,46(1):192-205
Let be an integer, and , , be the vector space over the cyclic space . The purpose of this paper is two-fold. First, we obtain sufficient conditions on such that the inverse Fourier transform of generates a tight wavelet frame in . We call these sets (tight) wavelet frame sets. The conditions are given in terms of multiplicative and translational tilings, which is analogous with Theorem 1.1 ([20]) by Wang in the setting of finite fields. In the second part of the paper, we exhibit a constructive method for obtaining tight wavelet frame sets in , , q an odd prime and (mod 4). 相似文献
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《Discrete Mathematics》2019,342(5):1233-1244
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We obtain upper bounds for the Steklov eigenvalues of a smooth, compact, n-dimensional submanifold M of Euclidean space with boundary Σ that involve the intersection indices of M and of Σ. One of our main results is an explicit upper bound in terms of the intersection index of Σ, the volume of Σ and the volume of M as well as dimensional constants. By also taking the injectivity radius of Σ into account, we obtain an upper bound that has the optimal exponent of k with respect to the asymptotics of the Steklov eigenvalues as . 相似文献