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101.
We show in the smooth category that the heat trace asymptotics and the heat content asymptotics can be made to grow arbitrarily rapidly. In the real analytic context, however, this is not true and we establish universal bounds on their growth. 相似文献
102.
We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube. 相似文献
103.
本文借助于HKp 空间上的积分,引进了IHKp 函数类的概念,讨论了IHKp函数类的刻划,以及其上算子和有界算子的刻划 相似文献
104.
Dragan Vukoti? 《Journal of Mathematical Analysis and Applications》2005,311(1):377-380
A theorem and a corollary in the paper cited in the title were stated incorrectly, as was pointed out by Christopher Hammond. We now state correctly and prove both of them. These results still generalize and explain the geometric meaning of the Cowen-Hurst norm formula. We also include additional references and provide an example relevant for further study. 相似文献
105.
106.
§1.IntroductionLetTbealinear,boundedoperatoractingonacomplex,separable,infinitedimensionalHibertspaceH.Wecal(U+K)(T)={RTR-1,R... 相似文献
107.
M. Hasanov 《Journal of Mathematical Analysis and Applications》2008,342(2):766-772
Basis problems for self-adjoint matrix valued functions are studied. We suggest a new and nonstandard method to solve basis problems both in finite and infinite dimensional spaces. Although many results in this paper are given for operator functions in infinite dimensional Hilbert spaces, but to demonstrate practicability of this method and to present a full solution of basis problems, in this paper we often restrict ourselves to matrix valued functions which generate Rayleigh systems on the n-dimensional complex space Cn. The suggested method is an improvement of an approach given recently in our paper [M. Hasanov, A class of nonlinear equations in Hilbert space and its applications to completeness problems, J. Math. Anal. Appl. 328 (2007) 1487-1494], which is based on the extension of the resolvent of a self-adjoint operator function to isolated eigenvalues and the properties of quadratic forms of the extended resolvent. This approach is especially useful for nonanalytic and nonsmooth operator functions when a suitable factorization formula fails to exist. 相似文献
108.
Liu Xiyu 《数学学报(英文版)》1998,14(1):125-134
This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous
media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary
value problems.
This work is supported in part by NSF of Shandong Province and NNSF of China 相似文献
109.
In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness. 相似文献
110.
George Voutsadakis 《Mathematical Logic Quarterly》2007,53(2):147-161
The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first‐order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality‐free first‐order structures are provided in the framework of structure systems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献