共查询到20条相似文献,搜索用时 31 毫秒
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《Expositiones Mathematicae》2020,38(2):180-201
We give a new proof of a theorem of Weyl on the continuous part of the spectrum of Sturm–Liouville operators on the half-line with asymptotically constant coefficients. Earlier arguments, due to Weyl and Kodaira, depended on particular features of Green’s functions for linear ordinary differential operators. We use a concept of asymptotic containment of -algebra representations that has geometric origins. We apply the concept elsewhere to the Plancherel formula for spherical functions on reductive groups. 相似文献
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We are concerned with the well-posedness theory of two-dimensional compressible subsonic jet flow issuing from a semi-infinitely long nozzle of arbitrary cross-section. Given any atmospheric pressure , we show that there exists a critical mass flux depending on and Ω, such that if the incoming mass flux is less than the critical value, then there exists a unique smooth subsonic jet flow, issuing from the given nozzle. The jet boundary is a free streamline, which initiates from the end point of the nozzle smoothly and extends to the infinity. One of the key observations in this paper is that the restriction of the incoming mass flux guarantees completely the subsonicity of the compressible jet in the whole flow field, which coincides with the observation on the compressible subsonic flows in an infinitely long nozzle without free boundary in [8]. 相似文献
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Van Hoang Nguyen 《Journal of Functional Analysis》2021,280(3):108833
In this paper, we prove the existence of maximizers for the sharp Moser–Trudinger type inequalities in whole space , with more general nonlinearity. The main key in our proof is a precise estimate of the concentrating level of the Moser–Trudinger functional associated with our inequalities on the normalized concentrating sequences. This estimate solves a heavily non-trivial and open problem related to the sharp Moser–Trudinger inequality. Our method gives an alternative proof of the existence of maximizers for the Moser–Trudinger inequality and singular Moser–Trudinger inequality in whole space due to Li and Ruf [30] and Li and Yang [31] without using blow-up analysis argument. 相似文献
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We consider a generalisation of a conjecture by Patterson and Wiedemann from 1983 on the Hamming distance of a function from to to the set of affine functions from to . We prove the conjecture for each q such that the characteristic of lies in a subset of the primes with density 1 and we prove the conjecture for all q by assuming the generalised Riemann hypothesis. Roughly speaking, we show the existence of functions for which the distance to the affine functions is maximised when n tends to infinity. This also determines the asymptotic behaviour of the covering radius of the Reed-Muller code over and so answers a question raised by Leducq in 2013. Our results extend the case , which was recently proved by the author and which corresponds to the original conjecture by Patterson and Wiedemann. Our proof combines evaluations of Gauss sums in the semiprimitive case, probabilistic arguments, and methods from discrepancy theory. 相似文献
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《Indagationes Mathematicae》2021,32(1):151-192
Motivated by applications to multiplicity formulas in index theory, we study a family of distributions associated to a piecewise quasi-polynomial function . The family is indexed by an integer , and admits an asymptotic expansion as , which generalizes the expansion obtained in the Euler–Maclaurin formula. When is the multiplicity function arising from the quantization of a symplectic manifold, the leading term of the asymptotic expansion is the Duistermaat–Heckman measure. Our main result is that is uniquely determined by a collection of such asymptotic expansions. We also show that the construction is compatible with pushforwards. As an application, we describe a simpler proof that formal quantization is functorial with respect to restrictions to a subgroup. 相似文献
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Ciprian A. Tudor Nakahiro Yoshida 《Stochastic Processes and their Applications》2019,129(9):3499-3526
We develop the asymptotic expansion theory for vector-valued sequences of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence . Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of and we illustrate our results by several examples. 相似文献
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Let be the number of monochromatic copies of a fixed connected graph in a uniformly random coloring of the vertices of the graph . In this paper we give a complete characterization of the limiting distribution of , when is a converging sequence of dense graphs. When the number of colors grows to infinity, depending on whether the expected value remains bounded, either converges to a finite linear combination of independent Poisson variables or a normal distribution. On the other hand, when the number of colors is fixed, converges to a (possibly infinite) linear combination of independent centered chi-squared random variables. This generalizes the classical birthday problem, which involves understanding the asymptotics of , the number of monochromatic -cliques in a complete graph (-matching birthdays among a group of friends), to general monochromatic subgraphs in a network. 相似文献
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A revised Yau's Curvature Difference Flow is considered to deform one convex curve to another one . It is proved that this flow exists globally on time interval and the evolving curve, preserving its convexity and bounded area A, converges to a fixed limiting curve (congruent to ) as time tends to infinity, where is the area bounded by the target curve . 相似文献
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《Journal of Functional Analysis》2023,284(6):109828
This paper is twofold. The first part aims to study the long-time asymptotic behavior of solutions to the heat equation on Riemannian symmetric spaces of noncompact type and of general rank. We show that any solution to the heat equation with bi-K-invariant initial data behaves asymptotically as the mass times the fundamental solution, and provide a counterexample in the non bi-K-invariant case. These answer problems recently raised by J.L. Vázquez. In the second part, we investigate the long-time asymptotic behavior of solutions to the heat equation associated with the so-called distinguished Laplacian on . Interestingly, we observe in this case phenomena which are similar to the Euclidean setting, namely asymptotic convergence with no bi-K-invariance condition and strong convergence. 相似文献
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