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151.
Matrix Schur product is the entry-wise product of matrices of the same size. It was shown by P. Chaisuriya and S.-C. Ong [1] that (forr453/xxlarge8805.gif" alt="ge" align="MIDDLE" BORDER="0">1) infinite matrices [a
jk
] such that [|a
jk
|
r
] 453/xxlarge603.gif" alt="epsiv" align="BASELINE" BORDER="0">B(l
2 form a Banach algebra under the norm 453/xxlarge8214.gif" alt="Verbar" align="MIDDLE" BORDER="0">[a
jk
]453/xxlarge8214.gif" alt="Verbar" align="MIDDLE" BORDER="0">
r
=453/xxlarge8214.gif" alt="Verbar" align="MIDDLE" BORDER="0">[|a
jk
|
r
]453/xxlarge8214.gif" alt="Verbar" align="MIDDLE" BORDER="0">1/r
and the Schur product. In this paper we demonstrate the existence of Banach space duality within the class of these algebras which is analogous to the classical duality between the spaces of compact, trace class, and bounded operators onl
2. Also we obtain a general functional calculus on these algebras, which is used to determine the spectrum and to justify the notion of 453/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">-norm introduced in [1].This author's research was supported by a sabbatical leave and a Division grant from Colby College.This author's research was supported by a research professorship at Central Michigan University.This author's research was supported by a visiting professorship at Central Michigan University. 相似文献
152.
We deal with variational problems on varying manifolds in ℝn. We represent each manifold by a positive measure μ, to which we associate a suitable notion of tangent space Tμ, of mean
curvature H(μ), and of Sobolev spaces with respect to μ on an open subset Ω ⊆ ℝn. We introduce the notions of weak and strong convergence for functions defined on varying manifolds, that is defined μh -a.e., being {μh} a weakly convergent sequence of measures. In this setting, we prove a strong-weak type compactness theorem for the pairs
(Pμ
h H(μh)), where Pμ
h are the projectors onto the tangent spaces Tμ
h. When μh belong to a suitable class of k-dimensional measures, having in particular a prescribed (k−1)-manifold as a boundary, we
enforce this result to study the convergence of energy functionals, possibly with a Dirichlet condition on ∂Ω. We also address
a perspective for optimization problems where the control variable is represented by a manifold with a prescribed boundary. 相似文献
153.
A. N. Karapetyants V. S. Rabinovich N. L. Vasilevski 《Integral Equations and Operator Theory》2001,40(3):278-308
We describe the Fredholm symbol algebra for theC
*-algebra generated by two dimensional singular integral operators, acting onL
2(2), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin.These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.Rostov State University RussiaPartially supported by Russian Fund for Fundamental Investigations, RFFI-98-01-01-023, and by CONACYT project 32424-EPartially supported by CONACYT Project 27934-E, México. 相似文献
154.
In this paper we develop a theory of parabolic pseudodifferential operators in anisotropic spaces. We construct a symbolic calculus for a class of symbols globally defined on 45688j/xxlarge8477.gif" alt="Ropf" align="BASELINE" BORDER="0">
n+1×45688j/xxlarge8477.gif" alt="Ropf" align="BASELINE" BORDER="0">
n+1, and then develop a periodisation procedure for the calculus of symbols on the cylinder
45688j/20_2005_Article_BF01301465_TeX2GIFIE1.gif" alt="
$$\mathbb{T}^n $$
" align="middle" border="0">
×45688j/xxlarge8477.gif" alt="Ropf" align="BASELINE" BORDER="0">. We show Gårding's inequality for suitable operators and precise estimates for the essential norm in anisotropic Sobolev spaces. These new mapping properties are needed in localization arguments for the analysis of numerical approximation methods. 相似文献
155.
Silvano Delladio 《Journal of Geometric Analysis》2001,11(1):17-42
We show that the L
p
norm of the second fundamental form of hypersurfaces in
R
n+1
is very coercive in the GMT setting of Gauss graphs currents, when p exceeds the dimension n. A compactness result for immersed
hypersurfaces and its application to a variational problem are provided. 相似文献
156.
In this paper we find a relation between the lattice of hyperinvariant subspaces of an operatorT of classC
0 over a multiply connected region and that of its Jordan modelT. It is shown that, generally, the lattice corresponding toT can be identified with a retract of that corresponding toT. Thus the Jordan model has the smallest lattice of hyperinvariant subspaces in a given quasisimilarity class. 相似文献
157.
Stanisław Lewanowicz Eduardo Godoy Iván Area André Ronveaux Alejandro Zarzo 《Numerical Algorithms》2000,23(1):31-50
We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect
to the q-classical orthogonal polynomials pk(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization
of ϑm(x) pn(x;q), where ϑm(x) is xmor (x;q)m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
158.
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
159.
We compute the Dijkgraaf–Witten invariants of surfaces in terms of projective representations of groups. As an application we prove that the complex Dijkgraaf–Witten invariants of surfaces of positive genus are positive integers. 相似文献
160.
《Quaestiones Mathematicae》2013,36(1-3):295-307
Abstract We define a new class B of sets of strongly summable and bounded sequences, determine their first and second α- and β-duals, and characterize linear operators on the spaces in B. 相似文献