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151.
Lech Zielinski 《Mathematical Physics, Analysis and Geometry》1999,2(3):291-321
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients. 相似文献
152.
153.
J.?Vigo-AguiarEmail author R.?Ardanuy-Albajar Bruce?A.?Wade 《Journal of Mathematical Modelling and Algorithms》2005,4(3):317-330
Using an equivalent expression for solutions of second order Dirichlet problems in terms of Ito type stochastic differential
equations, we develop a numerical solution method for Dirichlet boundary value problems. It is possible with this idea to
solve for solution values of a partial differential equation at isolated points without having to construct any kind of mesh
and without knowing approximations for the solution at any other points. Our method is similar to a recently published approach,
but differs primarily in the handling of the boundary. Some numerical examples are presented, applying these techniques to
model Laplace and Poisson equations on the unit disk.
Visiting Professor, Universidad de Salamanca. 相似文献
154.
Brice Camus 《Journal of Functional Analysis》2004,217(1):79-102
We study the semi-classical trace formula at a critical energy level for a h-pseudo-differential operator on whose principal symbol has a totally degenerate critical point for that energy. We compute the contribution to the trace formula of isolated non-extremum critical points under a condition of “real principal type”. The new contribution to the trace formula is valid for all time in a compact subset of but the result is modest since we have restrictions on the dimension. 相似文献
155.
Kumi Yasuda 《Journal of Functional Analysis》2004,216(2):422-454
This article aims at showing a p-adic analogue of Selberg's trace formula, which describes a duality between the spectrum of a Hilbert-Schmidt operator and the length of prime geodesics appearing in the p-adic upper half-plane associated with a hyperbolic discontinuous subgroup of . Then we construct Markov processes on the fundamental domain relative to such subgroups, to whose transition operators the trace formula applied and a p-adic analogue of prime geodesic theorem is proved. 相似文献
156.
Nicolas Dutertre 《Geometriae Dedicata》2004,105(1):43-59
We establish a Gauss—Bonnet type formula for a smooth fibre of a nonproper real polynomial of
n
. For this we need to study topological properties of a generic hyperplane section of this fibre. 相似文献
157.
158.
In this paper we study the local behaviour of a trigonometric polynomial around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form are also proved.
159.
We demonstrate that an idea related to the Central Limit Theorem and approximations by accompanying laws in probability theory is useful to get optimal convergence rates in some approximation formulas for operators. As examples we provide a bound for Euler approximations of bounded holomorphic semigroups; a bound for error in approximation of a power of operators by accompanying exponents, which is a useful tool in analysis of the Trotter–Kato formula, and can be considered as an extended version of Chernoff's
lemma. 相似文献
160.
Robert S. Maier 《Journal of statistical physics》2003,111(5-6):1027-1048
Several formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts's formula for the horizontal-vertical crossing probability and Cardy's new formula for the expected number of crossing clusters. It is shown that for lattices where conformal invariance holds, they simplify when the spatial domain is taken to be the interior of an equilateral triangle. The two crossing functions can be expressed in terms of an equianharmonic elliptic function with a triangular rotational symmetry. This suggests that rigorous proofs of Watts's formula and Cardy's new formula will be easiest to construct if the underlying lattice is triangular. The simplification in a triangular domain of Schramm's bulk Cardy's formula is also studied. 相似文献