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991.
By the method of geometry of Banach spaces, we have proven that a bounded linear operator in Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rank bounded homogeneous operators, which reveals the essence of the counter example given by Enflo. 相似文献
992.
D. A. Popov 《Functional Analysis and Its Applications》2003,37(3):215-220
We consider the problem of reconstructing a function on the disk
from its integrals over curves close to straight lines, i.e., the inversion problem for the generalized Radon transform. Necessary and sufficient conditions on the range of the generalized Radon transform are obtained for functions supported in a smaller disk
under the additional condition that the curves that do not meet
coincide with the corresponding straight lines. 相似文献
993.
We study the limit behavior of the spectral characteristics of truncated multidimensional integral operators whose kernels are homogeneous of degree –n and invariant under the rotation group SO(n). We prove that the limit of the -pseudospectra of the truncated operators K
as 0 is equal to the union of the -pseudospectra of the original operator K and the transposed operator
. 相似文献
994.
Let
be a compact set with interior G. Let L
1
(G,dx), >0 dx-a.e. on G, and m:=dx. Let A=(a
ij
) be symmetric, and globally uniformly strictly elliptic on G. Let be such that
; f,
, is closable in L
2
(G,m) with closure (
r
,D(
r
)). The latter is fulfilled if satisfies the Hamza type condition, or
i
L
1
loc
(G,dx), 1id. Conservative, non-symmetric diffusion processes X
t
related to the extension of a generalized Dirichlet form
where
satisfies
are constructed and analyzed. If G is a bounded Lipschitz domain, H
1,1
(G), and a
ij
D(
r
), a Skorokhod decomposition for X
t
is given. This happens through a local time that is uniquely associated to the smooth measure 1{
Tr
()>0}
d, where Tr denotes the trace and the surface measure on G.This research has been financially supported by TMR grant HPMF-CT-2000-00942 of the European Union.
Mathematics Subject Classification (2000): 60J60, 60J55, 31C15, 31C25, 35J25 相似文献
995.
In several complex variables, the multivariate Padé-type approximation theory is based on the polynomial interpolation of the multidimensional Cauchy kernel and leads to complicated computations. In this paper, we replace the multidimensional Cauchy kernel by the Bergman kernel function K
(z,x) into an open bounded subset of C
n
and, by using interpolating generalized polynomials for K
(z,x), we define generalized Padé-type approximants to any f in the space OL
2() of all analytic functions on which are of class L
2. The characteristic property of such an approximant is that its Fourier series representation with respect to an orthonormal basis for OL
2() matches the Fourier series expansion of f as far as possible. After studying the error formula and the convergence problem, we show that the generalized Padé-type approximants have integral representations which give rise to the consideration of an integral operator – the so-called generalized Padé-type operator – which maps every f
OL
2() to a generalized Padé-type approximant to f. By the continuity of this operator, we obtain some convergence results about series of analytic functions of class L
2. Our study concludes with the extension of these ideas into every functional Hilbert space H and also with the definition and properties of the generalized Padé-type approximants to a linear operator of H into itself. As an application we prove a Painlevé-type theorem in C
n
and we give two examples making use of generalized Padé-type approximants. 相似文献
996.
Mbekhta's subspaces and a spectral theory of compact operators 总被引:4,自引:0,他引:4
Let be an operator on an infinite-dimensional complex Banach space. By means of Mbekhta's subspaces and , we give a spectral theory of compact operators. The main results are: Let be compact. . The following assertions are all equivalent: (1) 0 is an isolated point in the spectrum of (2) is closed; (3) is of finite dimension; (4) is closed; (5) is of finite dimension; . sufficient conditions for to be an isolated point in ; . sufficient and necessary conditions for to be a pole of the resolvent of .
997.
Franç ois Germinet Abel Klein 《Proceedings of the American Mathematical Society》2003,131(3):911-920
We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of mathematical physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved Combes-Thomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than any polynomial.
998.
Nina Zorboska 《Proceedings of the American Mathematical Society》2003,131(3):793-800
We analyze the connection between compactness of operators on the Bergman space and the boundary behaviour of the corresponding Berezin transform. We prove that for a special class of operators that we call radial operators, an oscilation criterion is a sufficient condition under which the compactness of an operator is equivalent to the vanishing of the Berezin transform on the unit circle. We further study a special class of radial operators, i.e., Toeplitz operators with a radial symbol.
999.
Fré dé ric Bayart 《Proceedings of the American Mathematical Society》2003,131(6):1789-1791
We study the composition operators which are similar to an isometry on the classical Hardy space .
1000.
A note on the spectrum of an upper triangular operator matrix 总被引:1,自引:0,他引:1
Mohamed Barraa Mohamed Boumazgour 《Proceedings of the American Mathematical Society》2003,131(10):3083-3088
Let be a upper triangular operator matrix acting on the Banach space . We investigate the set of the operators for which , where denotes the spectrum.