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81.
Given an admissible measure μ on where is an open set, we define a realization of the Laplacian in with general Robin boundary conditions and we show that generates a holomorphic C
0
-semigroup on which is sandwiched by the Dirichlet Laplacian and the Neumann Laplacian semigroups. Moreover, under a locality and a regularity
assumption, the generator of each sandwiched semigroup is of the form . We also show that if contains smooth functions, then μ is of the form (where σ is the (n-1)-dimensional Hausdorff measure and β a positive measurable bounded function on ); i.e. we have the classical Robin boundary conditions.
RID="h1"
ID="h1"Dédié à Philippe Bénilan
RID="*"
ID="h1"This work is part of the DGF-Project: "Regularit?t und Asymptotik für elliptische und parabolische Probleme". 相似文献
82.
In [9] we introduced the notion of equilibrium surface current JdSx on the closed C smooth surfaces in R
3 as a generalization of electric solenoid, and proved their existence. We here show an algorithm for JdSx starting from a given surface current J dSx on . 相似文献
83.
It is shown that the residue expansion of an elliptic Selberg integral gives rise to an integral representation for a multiple modular hypergeometric series. A conjectural evaluation formula for the integral then implies a closed summation formula for the series, generalizing both the multiple basic hypergeometric 87 sum of Milne-Gustafson type and the (one-dimensional) modular hypergeometric 87 sum of Frenkel and Turaev. Independently, the modular invariance ensures the asymptotic correctness of our multiple modular hypergeometric summation formula for low orders in a modular parameter. 相似文献
84.
Florian Luca. 《Mathematics of Computation》2001,70(234):893-896
For any , let be the th prime number. In this paper, we confirm a conjecture of Erdos and Stewart concerning all the solutions of the diophantine equation , when .
85.
Another Note on the Greatest Prime Factors of Fermat Numbers 总被引:1,自引:0,他引:1
For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if Fm = 22m + 1 is the mth Fermat number, then P(Fm) 2m+2(4m + 9) + 1 for all m 4. We also give a lower bound of a similar type for P(Fa,m), where Fa,m = a2m + 1 whenever a is even and m a18.AMS Subject Classification (1991) 11A51 11J86 相似文献
86.
We improve on a recent result of Saradha giving a transcendence measure for the quotient
of a period of an elliptic curve defined over by its associated quasi-period. In an (almost successful) attempt to include in a single measure both this result and that obtained by Reyssat in 1980, we blend into the modular method ideas related to modular but also hypergeometric functions, as appearing e.g. in André's work, as well as some Galois considerations. 相似文献
87.
In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g)
S
= V(f) A
V(g)
T
+ <u, f
(N)
g
(N)V(f) =(f(c
0), f "(c
0), ..., f
(n – 1)
0(c
0), ..., f(c
p
), f "(c
p
), ..., f
(n – 1)
p(c
p
))
u is a regular linear functional on the linear space P of real polynomials, c
0, c
1, ..., c
p
are distinct real numbers, n
0, n
1, ..., n
p
are positive integer numbers, N=n
0+n
1+...+n
p
, and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation. 相似文献
88.
Densely Continuous Forms in Vietoris Hyperspaces 总被引:2,自引:0,他引:2
R. A. McCoy 《Set-Valued Analysis》2000,8(3):267-271
For countably paracompact normal spaces X and locally compact separable metric spaces Y, a characterization is given for the closure of the set of densely continuous forms from X to Y in the hyperspace of nonempty closed subsets of X × Y under the Vietoris topology. This shows that for such X having no isolated points, every closed subset of X × R that is dense over X can be Vietoris approximated by a semicontinuous function on X. 相似文献
89.
We deal with the 2‐orthogonal, 2‐symmetric self‐associated sequence (2‐orthogonal Tchebychev polynomials) and its cubic components.
We prove that all the forms (linear functionals) arising are third degree forms. Therefore, an introduction to third degree
forms is provided. We look for the connection between these components which are 2‐orthogonal with respect to the functional
vector t(w0{μ},w1
μ) and orthogonal sequences with respect to w0
μ, μ=0,1,2. Associated forms w0
μ)1) and their inverse w0
μ)-1 are also studied through the symmetrized w0}0
μ, μ=0,1,2. Further, we give integral representations for some of these forms.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
90.
Shamita Dutta Gupta Xiaotie She 《Proceedings of the American Mathematical Society》2000,128(8):2203-2212
In this paper, we obtain an Euler product with functional equation associated to a noncuspidal metaplectic form on the double cover of . Zagier's idea of Rankin-Selberg method is used to define the convolution of and the -function.