共查询到20条相似文献,搜索用时 0 毫秒
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The author would like to thank Prof. S. Shatz and the University of Pennsylvania for their hospitality 相似文献
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Shmuel Kantorovitz 《Commentarii Mathematici Helvetici》1981,56(1):163-178
LetT be a possibly unbounded linear operator in the Banach spaceX such thatR(t)=(t+T)?1 is defined onR +. LetS=TR(I?TR) and letB(.,.) denote the Beta function. Theorem 1.1.T is a scalar-type spectral operator with spectrum in [0, ∞) if and only if $$sup\left\{ {B\left( {k,k} \right)^{ - 1} \int_0^\infty {\left| {x*S^k \left( t \right)x} \right|{{dt} \mathord{\left/ {\vphantom {{dt} t}} \right. \kern-\nulldelimiterspace} t};\left\| x \right\| \leqslant 1,} \left\| {x*} \right\| \leqslant 1,k \geqslant 1} \right\}< \infty .$$ A “local” version of this result is formulated in Theorem 2.2. 相似文献
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Let be a family of elliptic differential operators with unbounded coefficients defined in RN+1. In [M. Kunze, L. Lorenzi, A. Lunardi, Nonautonomous Kolmogorov parabolic equations with unbounded coefficients, Trans. Amer. Math. Soc., in press], under suitable assumptions, it has been proved that the operator G:=A−Ds generates a semigroup of positive contractions (Tp(t)) in Lp(RN+1,ν) for every 1?p<+∞, where ν is an infinitesimally invariant measure of (Tp(t)). Here, under some additional conditions on the growth of the coefficients of A, which cover also some growths with an exponential rate at ∞, we provide two different cores for the infinitesimal generator Gp of (Tp(t)) in Lp(RN+1,ν) for p∈[1,+∞), and we also give a partial characterization of D(Gp). Finally, we extend the results so far obtained to the case when the coefficients of the operator A are T-periodic with respect to the variable s for some T>0. 相似文献
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A.G. Ramm 《Journal of Mathematical Analysis and Applications》2007,325(1):490-495
Let A be a linear, closed, densely defined unbounded operator in a Hilbert space. Assume that A is not boundedly invertible. If Eq. (1) Au=f is solvable, and ‖fδ−f‖?δ, then the following results are provided: Problem Fδ(u):=‖Au−fδ‖2+α‖u‖2 has a unique global minimizer uα,δ for any fδ, uα,δ=A*−1(AA*+αI)fδ. There is a function α=α(δ), limδ→0α(δ)=0 such that limδ→0‖uα(δ),δ−y‖=0, where y is the unique minimal-norm solution to (1). A priori and a posteriori choices of α(δ) are given. Dynamical Systems Method (DSM) is justified for Eq. (1). 相似文献
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We prove that there are holomorphic functions in the Hardy space of the unit ball or the bidisc such that the big Hankel operator with symbol is bounded and for any holomorphic function the function cannot be bounded.
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The spectral order, a notion originated by Olson for bounded operators, is investigated here in the context of unbounded operators. Dissimilarities between bounded and unbounded cases are pointed out. New criteria for two operators to be comparable are supplied. A way of reducing the study of the spectral order to the case of bounded operators is proposed. Connections with essential selfadjointness are established. Integral inequalities for monotonically increasing functions are characterized in terms of distribution functions. Some illustrative examples are furnished. 相似文献
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Vladimir Manuilov Sergei Silvestrov 《Proceedings of the American Mathematical Society》2006,134(9):2593-2598
For a class of unbounded operators, a deformation of a Bott projection is used to construct an integer-valued invariant measuring deviation of the non-commutative deformations from the commutative originals, and its interpretation in terms of -theory of -algebras is given. Calculation of this invariant for specific important classes of unbounded operators is also presented.
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We consider unique continuation theorems for solution of inequalities with W allowed to be unbounded. We obtain two kinds of results. One allows W ? Lploc(n) with . The other requires fW2 to be ?Δ-form bounded for all f ? C0∞. 相似文献
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Wolfgang Arendt Giorgio Metafune 《Journal of Mathematical Analysis and Applications》2008,338(1):505-517
We consider a strictly elliptic operator
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We prove that a first-order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on with values in a reflexive Banach space if and only if the corresponding strongly continuous evolution family has exponential dichotomies on both and and a pair of the ranges of the dichotomy projections is Fredholm, and that the Fredholm index of G is equal to the Fredholm index of the pair. The operator G is the generator of the evolution semigroup associated with the evolution family. In the case when the evolution family is the propagator of a well-posed differential equation u′(t)=A(t)u(t) with, generally, unbounded operators , the operator G is a closure of the operator . Thus, this paper provides a complete infinite-dimensional generalization of well-known finite-dimensional results by Palmer, and by Ben-Artzi and Gohberg. 相似文献
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For bounded linear operators, the study ofWeyl-type theorems and properties has been of significant interest for several non-normal classes of operators. In this paper, we extend this study to a class of unbounded posinormal operators. We define and study the spectral properties of unbounded posinormal and totally posinormal operators defined on an infinite dimensional complex Hilbert space H. For this class, under certain conditions several Weyl-type theorems and related properties are obtained. 相似文献
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Alberto Farina Matteo Novaga Andrea Pinamonti 《NoDEA : Nonlinear Differential Equations and Applications》2014,21(6):869-883
We prove the one-dimensional symmetry of solutions to elliptic equations of the form ?div(e G(x) a(|?u|)?u) = f(u) e G(x), under suitable energy conditions. Our results holds without any restriction on the dimension of the ambient space. 相似文献
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A. Lunardi G. Metafune D. Pallara 《Proceedings of the American Mathematical Society》2005,133(9):2625-2635
We study the realisation of the operator in with Dirichlet boundary condition, where is a possibly unbounded open set in , is a semi-convex function and the measure lets be formally self-adjoint. The main result is that at is a dissipative self-adjoint operator in .
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We construct dense sets of hypercyclic vectors for unbounded differention operators, including differentiation operators on the Hardy spaceH
2, and the Laplacian operator onL
2((), for any bounded open subset of 2. Furthermore, we show that these operators are chaotic, in the sense of Devaney. 相似文献
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John B. Conway Kyung Hee Jin Sherwin Kouchekian 《Journal of Mathematical Analysis and Applications》2003,279(2):418-429
This paper explores properties of the Bergman operator on unbounded open subsets of the plane. In addition to the characterization of the bounded commutant of such operators it proves the Berger-Shaw theorem and gives some general criteria under which the operator and its self-commutator are densely defined. 相似文献
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A minimal normal extension of unbounded subnormal operators is established and characterized and spectral inclusion theorem
is proved. An inverse Cayley transform is constructed to obtain a closed unbounded subnormal operator from a bounded one.
Two classes of unbounded subnormals viz analytic Toeplitz operators and Bergman operators are exhibited. 相似文献