共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider the Cauchy problem for the Helmholtz equation in an arbitrary bounded planar domain with Cauchy data only on part of the boundary of the domain. We derive a Carleman-type formula for a solution to this problem and give a conditional stability estimate. 相似文献
2.
Let Δ be an equilateral cone in C with vertices at the complex numbers and rigid base M (Section 1). Assume that the positive real semi-axis is the bisectrix of the angle at the origin. For the base M of the cone Δ we derive a Carleman formula representing all those holomorphic functions from their boundary values (if they exist) on M which belong to the class . The class is the class of holomorphic functions in Δ which belong to the Hardy class near the base M (Section 2). As an application of the above characterization, an important result is an extension theorem for a function fL1(M) to a function . 相似文献
3.
Sh. Yarmukhamedov 《Mathematical Notes》2008,83(5-6):693-706
In this paper, we propose an explicit formula for the reconstruction of a harmonic function in the domain from its known values and from the values of its normal derivative on part of the boundary, i.e., we give an explicit continuation and a regularization formula of the solution of the Cauchy problem for the Laplace equation. 相似文献
4.
We establish an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit solution to the Cauchy problem for the Laplace equation. 相似文献
5.
Sh. Yarmukhamedov 《Siberian Mathematical Journal》2001,43(1):183-193
We establish an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit solution to the Cauchy problem for the Laplace equation. 相似文献
6.
7.
By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes. 相似文献
8.
We consider the spectrally negative L@vy processes and determine the joint laws for the quantities such as the first and last passage times over a fixed level, the overshoots and undershoots at first passage, the minimum, the maximum, and the duration of negative values. We apply our results to insurance risk theory to find an explicit expression for the generalized expected discounted penalty function in terms of scale functions. Furthermore, a new expression for the generalized Dickson's formula is provided. 相似文献
9.
Stephen Simons 《Proceedings of the American Mathematical Society》2006,134(10):2983-2987
In this paper, we obtain an explicit formula for the interior of the domain of a maximal monotone multifunction in terms of its Fitzpatrick function.
10.
11.
In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl(Vn,n) is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl(Vn,n) are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained. 相似文献
12.
In this paper we consider scalar convex conservation laws in one space variable in a stripD =(x, t): 0 ≤x ≤1,t > 0 and obtain an explicit formula for the solution of the mixed initial boundary value problem, the boundary data being
prescribed in the sense of Bardos-Leroux and Nedelec. We also get an explicit formula for the solution of weighted Burgers
equation in a strip. 相似文献
13.
LUK Hing-Sun 《中国科学A辑(英文版)》2006,(11)
This paper gives an explicit formula for calculating the Webster pseudo torsion for a strictly pseudoconvex pseudo-hermitian hypersurface. As applications, we are able to classify some pseudo torsion-free hypersurfaces, which include real ellipsoids. 相似文献
14.
给出关于带限函数的小波变换的一类新的反演公式,这个公式具有比熟知的结果更清晰的表达式,并且含有可以自由选择的因子。 相似文献
15.
Steven G. Krantz Harold R. Parks 《Journal of Mathematical Analysis and Applications》2008,340(2):1263-1270
The classical Lagrange inversion theorem is a concrete, explicit form of the implicit function theorem for real analytic functions. An explicit construction shows that the formula is not true for all merely smooth functions. The authors modify the Lagrange formula by replacing the smooth function by its Maclaurin polynomials. The resulting modified Lagrange series is, in analogy to the Maclaurin polynomials, an approximation to the solution function accurate to o(xN) as x→0. 相似文献
16.
Feng Qi 《Indagationes Mathematicae》2018,29(5):1179-1192
In the paper, the author introduces a new notion “multivariate logarithmic polynomial”, establishes two recurrence relations, an explicit formula, and an identity for multivariate logarithmic polynomials by virtue of the Faà di Bruno formula and two identities for the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, some product inequalities, and logarithmic convexity for multivariate logarithmic polynomials by virtue of some properties of completely monotonic functions. 相似文献
17.
Hans Rullgård 《Arkiv f?r Matematik》2004,42(2):353-362
We derive a direct inversion formula for the exponential Radon transform. Our formula requires only the values of the transform
over an 180° range of angles. It is an explicit formula, except that it involves a holomorphic function for which an explicit
expression has not been found. In practice, this function can be approximated by an easily computed polynomial of rather low
degree. 相似文献
18.
We consider the Hermite trigonometric interpolation problem of order 1 for equidistant nodes, i.e., the problem of finding a trigonometric polynomial t that interpolates the values of a function and of its derivative at equidistant points. We give a formula for the Fourier coefficients of t in terms of those of the two classical trigonometric polynomials interpolating the values and those of the derivative separately. This formula yields the coefficients with a single FFT. It also gives an aliasing formula for the error in the coefficients which, on its turn, yields error bounds and convergence results for differentiable as well as analytic functions. We then consider the Lagrangian formula and eliminate the unstable factor by switching to the barycentric formula. We also give simplified formulae for even and odd functions, as well as consequent formulae for Hermite interpolation between Chebyshev points. 相似文献
19.
I. V. Shestakov 《Russian Mathematics (Iz VUZ)》2009,53(7):43-54
In this paper we consider the Cauchy problem as a typical example of ill-posed boundary-value problems. We obtain the necessary and (separately) sufficient conditions for the solvability of the Cauchy problem for a Dirac operator A in Sobolev spaces in a bounded domain D ? ? n with a piecewise smooth boundary. Namely, we reduce the Cauchy problem for the Dirac operator to the problem of harmonic extension from a smaller domain to a larger one. Moreover, along with the solvability conditions for the problem, using bases with double orthogonality, we construct a Carleman formula for recovering a function u in a Sobolev space H s (D), s ∈ ?, from its values on Γ and values Au in D, where Γ is an open connected subset of the boundary ?D. It is worth pointing out that we impose no assumptions about geometric properties of the domain D, except for its connectedness. 相似文献
20.
A. Connes 《Selecta Mathematica, New Series》1999,5(1):29-106
We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual
noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number theory as a
trace formula on the noncommutative space of Adele classes. This reduces the Riemann hypothesis to the validity of the trace
formula and eliminates the parameter of our previous approach. 相似文献