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1.
We analyze a class of quasilinear elliptic problems involving a p(·)-Laplace-type operator on a bounded domain
W ì \mathbb RN{\Omega\subset{\mathbb R}^N}, N ≥ 2, and we deal with nonlinear conditions on the boundary. Working on the variable exponent Lebesgue–Sobolev spaces, we
follow the steps described by the “fountain theorem” and we establish the existence of a sequence of weak solutions. 相似文献
2.
We give state space formulas for a (“central”) solution of the suboptimal Nehari problem for functions defined on the unit
disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming exponential stability,
we assume a weaker stability concept (the combination of input-, output- and input-output stability), which allows us to solve
the problem for general H-infinity functions.
相似文献
3.
We make a contribution to the theory of embeddings of anisotropic Sobolev spaces into L
p
-spaces (Sobolev case) and spaces of H?lder continuous functions (Morrey case). In the case of bounded domains the generalized
embedding theorems published so far pose quite restrictive conditions on the domain’s geometry (in fact, the domain must be
“almost rectangular”). Motivated by the study of some evolutionary PDEs, we introduce the so-called “semirectangular setting”,
where the geometry of the domain is compatible with the vector of integrability exponents of the various partial derivatives,
and show that the validity of the embedding theorems can be extended to this case. Second, we discuss the a priori integrability
requirement of the Sobolev anisotropic embedding theorem and show that under a purely algebraic condition on the vector of
exponents, this requirement can be weakened. Lastly, we present a counterexample showing that for domains with general shapes
the embeddings indeed do not hold. 相似文献
4.
The main goal of the article is to show that Paley-Wiener functions ƒ ∈ L
2(M) of a fixed band width to on a Riemannian manifold of bounded geometry M completely determined and can be reconstructed
from a set of numbers Φi (ƒ), i ∈ ℕwhere Φi
is a countable sequence of weighted integrals over a collection of “small” and “densely” distributed compact subsets. In particular, Φi, i ∈ ℕ,can be a sequence of weighted Dirac measures δxi, xi ∈M.
It is shown that Paley-Wiener functions on M can be reconstructed as uniform limits of certain variational average spline
functions.
To obtain these results we establish certain inequalities which are generalizations of the Poincaré-Wirtingen and Plancherel-Polya
inequalities.
Our approach to the problem and most of our results are new even in the one-dimensional case. 相似文献
5.
There is a subtle difference as far as the invariant subspace problem is concerned for operators acting on real Banach spaces
and operators acting on complex Banach spaces. For instance, the classical hyperinvariant subspace theorem of Lomonosov [Funktsional. Anal. nal. i Prilozhen 7(3)(1973), 55–56. (Russian)], while true for complex Banach spaces is false for real Banach spaces. When one starts with a
bounded operator on a real Banach space and then considers some “complexification technique” to extend the operator to a complex
Banach space, there seems to be no pattern that indicates any connection between the invariant subspaces of the “real” operator
and those of its “complexifications.” The purpose of this note is to examine two complexification methods of an operator T acting on a real Banach space and present some questions regarding the invariant subspaces of T and those of its complexifications
Mathematics Subject Classification 1991: 47A15, 47C05, 47L20, 46B99
Y.A. Abramovich: 1945–2003
The research of Aliprantis is supported by the NSF Grants EIA-0075506, SES-0128039 and DMI-0122214 and the DOD Grant ACI-0325846 相似文献
6.
Özgür Yilmaz 《Constructive Approximation》2002,18(4):599-623
We investigate the stability and robustness properties of a family of algorithms used to “coarsely quantize” bandlimited functions.
The algorithms we will consider are one-bit second-orderΣΔA-quantization schemes and some modified versions of these. We prove
that there exists a bounded region that remains positively invariant under the two-dimensional piecewise-affine discrete dynamical
system associated with each of these quantizers. Moreover, this bounded region can be constructed so that it is robust under
small changes in the quantizer. We also show some interesting properties of the resulting binary sequences. 相似文献
7.
Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared,
which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow “fast” with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the “curse
of dimensionality,” which often makes unfeasible traditional linear approximation techniques for functional optimization problems,
when admissible solutions depend on a large number d of variables.
Marcello Sanguineti was partially supported by a PRIN grant from the Italian Ministry for University and Research (project
“Models and Algorithms for Robust Network Optimization”). 相似文献
8.
This note contributes to a circle of ideas that we have been developing recently in which we view certain abstract operator
algebras H∞(E), which we call Hardy algebras, and which are noncommutative generalizations of classical H∞, as spaces of functions defined on their spaces of representations. We define a generalization of the Poisson kernel, which
“reproduces” the values, on , of the “functions” coming from H∞(E). We present results that are natural generalizations of the Poisson integral formula. They also are easily seen to be generalizations
of formulas that Popescu developed. We relate our Poisson kernel to the idea of a characteristic operator function and show
how the Poisson kernel identifies the “model space” for the canonical model that can be attached to a point in the disc . We also connect our Poisson kernel to various “point evaluations” and to the idea of curvature.
The first named author was supported in part by grants from the National Science Foundation and from the U.S.-Israel Binational
Science Foundation. The second named author was supported in part by the U.S.-Israel Binational Science Foundation and by
the B. and G. Greenberg Research Fund (Ottawa). 相似文献
9.
Mario Troisi 《Annali di Matematica Pura ed Applicata》1971,90(1):331-412
Summary We are concerned with non-variational boundary value problems, with omogeneus boundary conditions, for linear partial differential
equations of quasi-elliptic type in a bounded domain Θ in Rn.
It is well known that some of difficulties which arise in treating such problems, in comparison with ? regular ? elliptic
problems, are connected with the presence of angular points in Θ: let us point out withB. Pini [32] that ? a bounded domain for which it is possible to assign a correct boundary value problem for a quasi-elliptic but
not elliptic equation always has angular points ?.
We suppose Θ is a cartesian product of a finite number of open sets and, in order to overcome the difficulties attached to
the presence of angular points in Θ, taking as a model the two previous papers[33], [34] devoted to elliptic problems with singular data, we investigate the problem within suitable Sobolev weight spaces, connected
with the angular points of Θ and included in the ones we have studied in[35]. Within such spaces we get existence and uniqueness theorems.
Lavoro eseguito con contributo del C. N. R.
Entrata in Redazione il 30 ottobre 1971. 相似文献
Lavoro eseguito con contributo del C. N. R.
Entrata in Redazione il 30 ottobre 1971. 相似文献
10.
LetM be a Hilbert module of holomorphic functions over a natural function algebraA(Ω), where Ω ⊆ ℂ
m
is a bounded domain. LetM
0 ⊆M be the submodule of functions vanishing to orderk on a hypersurfaceZ ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient
modulesQ =M ⊖M
0 The invariants are given explicitly in the particular case ofk = 2. 相似文献