共查询到20条相似文献,搜索用时 15 毫秒
2.
We study eigenvalues of positive definite kernels of L2 integral operators on unbounded real intervals. Under the assumptions of integrability and uniform continuity of the kernel
on the diagonal the operator is compact and trace class. We establish sharp results which determine the eigenvalue distribution
as a function of the smoothness of the kernel and its decay rate at infinity along the diagonal. The main result deals at
once with all possible orders of differentiability and all possible rates of decay of the kernel. The known optimal results
for eigenvalue distribution of positive definite kernels in compact intervals are particular cases. These results depend critically
on a 2-parameter differential family of inequalities for the kernel which is a consequence of positivity and is a differential
generalization of diagonal dominance. 相似文献
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Let J and ${{\mathfrak{J}}}$ be operators on a Hilbert space ${{\mathcal{H}}}$ which are both self-adjoint and unitary and satisfy ${J{\mathfrak{J}}=-{\mathfrak{J}}J}$ . We consider an operator function ${{\mathfrak{A}}}$ on [0, 1] of the form ${{\mathfrak{A}}(t)={\mathfrak{S}}+{\mathfrak{B}}(t)}$ , ${t \in [0, 1]}$ , where ${\mathfrak{S}}$ is a closed densely defined Hamiltonian ( ${={\mathfrak{J}}}$ -skew-self-adjoint) operator on ${{\mathcal{H}}}$ with ${i {\mathbb{R}} \subset \rho ({\mathfrak{S}})}$ and ${{\mathfrak{B}}}$ is a function on [0, 1] whose values are bounded operators on ${{\mathcal{H}}}$ and which is continuous in the uniform operator topology. We assume that for each ${t \in [0,1] \,{\mathfrak{A}}(t)}$ is a closed densely defined nonnegative (=J-accretive) Hamiltonian operator with ${i {\mathbb{R}} \subset \rho({\mathfrak{A}}(t))}$ . In this paper we give sufficient conditions on ${{\mathfrak{S}}}$ under which ${{\mathfrak{A}}}$ is conditionally reducible, which means that, with respect to a natural decomposition of ${{\mathcal{H}}}$ , ${{\mathfrak{A}}}$ is diagonalizable in a 2×2 block operator matrix function such that the spectra of the two operator functions on the diagonal are contained in the right and left open half planes of the complex plane. The sufficient conditions involve bounds on the resolvent of ${{\mathfrak{S}}}$ and interpolation of Hilbert spaces. 相似文献
5.
A unified class of linear positive operators has been defined. Using these operators some approximation estimates have been obtained for unbounded functions. For particular linear positive operators these results sharpen and improve the earlier estimates due to Fuhua Cheng (J. Approx. Theory, 1984) and Xiehua Sun (J. Approx. Theory, 1988). 相似文献
6.
We study the existence of positive solutions of the nonlinear equation u+f(,u)=0, in D with u=0 on D, where D is an unbounded domain in R
2 with a compact nonempty boundary D consisting of finitely many Jordan curves. The aim is to prove an existence result for the above equation in a general setting by using potential theory. 相似文献
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Letfbeanon-linearmeromorphicfunctiondefinedinthecomplexplaneC.TheFatousetF(f)offisthelargestsubsetofCwheretheiteratesfoffformanormalfamily.ThecomplementofF(f)iscalledtheJuliasetanddenotedbyJ(f).IfUisacomponentofF(f),thenf(U)iscontainedinsomecomponentofF(f)whichwedenotebyUn.IfUnnUrn=.foralln/m,thenUiscalledwandering.OtherwiseUiscalledeventuallyperiodic.Inparticular,ifUk=UforsomepENandUrn/Ufor0Sm
相似文献
9.
Siddhartha Sahi 《Annals of Combinatorics》2006,10(2):255-269
We describe a connection between discrete birth process and a certain family of multivariate interpolation polynomials. This
enables us to compute all asymptotic moments of the birth process, generalizing previously known results for the mean and
variance.
Received July 15, 2004 相似文献
10.
Tomas Sjödin 《Potential Analysis》2007,27(3):271-280
In the course of studying quadrature domains Gustafsson, Sakai and Shapiro were led to the question of whether it is the case
that the positive integrable harmonic functions on a bounded domain are dense among all positive harmonic functions (w.r.t.
uniform convergence on compact subsets). In this article we will show how such approximation problems are related to representing
measures on the Martin boundary, and then we use these results to give a counterexample to the question posed above.
This research was supported by Science Foundation Ireland under Grant 06/RFP/MAT057. 相似文献
11.
For a coinmutative senugoup (S, +, *) with involution and a function f : S → [0, ∞), the set S(f) of those p ≥ 0 such that fP is a positive definite function on S is a closed subsemigroup of [0, ∞) containing 0. For S = (IR, +, x* = -x) it may happen that S(f) = { kd : k ∈ N0 } for some d > 0, and it may happen that S(f) = {0} ? [d, ∞) for some d > O. If α > 2 and if S = (?, +, n* = -n) and f(n) = e?[n]α or S = (IN0, +, n* = n) and f(n) = enα, then S(f) ∪ (0, c) = ? and [d, ∞) ? S(f) for some d ≥; c > 0. Although (with c maximal and d minimal) we have not been able to show c = d in all cases, this equality does hold if S = ? and α ≥ 3.4. In the last section we give sinipler proofs of previously known results concerning the positive definiteness of x → e?||x||α on normed spaces. 相似文献
12.
Potential Analysis - In this paper, we will study the behavior of the space of positive harmonic functions associated with the random walk on a discrete group under the change of probability... 相似文献
13.
D. S. Lubinsky 《Constructive Approximation》2000,16(2):313-316
No abstract.
December 8, 1997. Date accepted: February 6, 1998. 相似文献
14.
Fangjun Xu 《Journal of Theoretical Probability》2013,26(2):541-556
We consider a class of continuous time Markov chains on ? d . These chains are the discrete space analogue of Markov processes with jumps. Under some conditions, as we show, harmonic functions associated with these Markov chains are Hölder continuous. 相似文献
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In this paper the authors develop a new approach to the problemof propagation of smallness for harmonic functionsin arbitrary domains, in Rn (n 2). The main result of thispaper is a certain logarithmic-convexity relation for the L2-normsof harmonic functions. As a consequence, new kinds of uniquenessresults for harmonic functions are obtained. The method worksalso for analytic functions in C, with Lp-norms (p > 0).1991 Mathematics Subject Classification 31B05. 相似文献
17.
In this paper we consider perturbations of symmetric Boolean functions \({{\sigma_{n,k_1}} +\ldots+{\sigma_{n,k_s}}}\) in n-variable and degree k s . We compute the asymptotic behavior of Boolean functions of the type $${\sigma_{n,k_1}} +\ldots+{\sigma_{n,k_s}} +F(X_1, . . . , X_j)$$ for j fixed. In particular, we characterize all the Boolean functions of the type $${\sigma_{n,k_1}} +\ldots+{\sigma_{n,k_s}} +F(X_1, . . . , X_j)$$ that are asymptotic balanced. We also present an algorithm that computes the asymptotic behavior of a family of Boolean functions from one member of the family. Finally, as a byproduct of our results, we provide a relation between the parity of families of sums of binomial coefficients. 相似文献
18.
Potential Analysis - Assume that a bounded domain Ω??N (N ≥ 2) has the property that there exists a signed measure µ with compact support in Ω such that, for every... 相似文献
19.
Jiecheng Chen 《Journal of Mathematical Analysis and Applications》2002,267(1):310-328
In this paper, we mainly set up a kind of representation theorem of harmonic functions on manifolds with Ricci curvature bounded below and study non-tangential limits of harmonic functions. 相似文献
20.
Prolate Spheroidal Wave Functions (PSWFs) are a well-studied subject with applications in signal processing, wave propagation, antenna theory, etc. Originally introduced in the context of separation of variables for certain partial differential equations, PSWFs became an important tool for the analysis of band-limited functions after the famous series of articles by Slepian et al. The popularity of PSWFs seems likely to increase in the near future, as band-limited functions become a numerical (as well as an analytical) tool. 相似文献