摘要:

AbstractWe use the method of self‐adjoint extensions to define a self‐adjoint operatorATas the singular perturbation of a given self‐adjoint operatorAby a singular operatorTon a Hilbert space.We also find the structure of a singular operatorQsuch that the singular perturbation ofA2byQsatisfies (A2)Q= (AT)2. We obtain the explicit form ofQin terms ofAandT. A definition of then‐th power for strictly positive symmetric operators is als

ISSN:0025-584X    

DOI:10.1002/mana.19951730102

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractFor two compact metric spacesXandY, we prove that the space of all bounded Bögel functions onX×Yis isometrically isomorphic with the completion of the blending function spaceM(X) ⊗C(Y)+ C(X) ⊗M(Y) with respect to a suitable norm. This solves a problem raised by G. Freud. HereM(Z) andC(Z) denote the spaces of all bounded and continuous functions on the metric space Z, respectively. Applications are given to some problems in so‐called blending approximation. All this is based on an abstract Jackson‐type theorem in terms of the entropy numbers ofXandYand the mixed modulus of s

ISSN:0025-584X    

DOI:10.1002/mana.19951730103

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractFinite interval convolution operators acting between Bessel potential spacesHspare studied in regard to Fredholm properties and invertibility. The Fourier transform of the kernel‐function of the operator is assumed to be piecewise continuous on R. An example from diffraction theory is include

ISSN:0025-584X    

DOI:10.1002/mana.19951730104

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this note we study a variational method of regularization to solve nonlinear ill‐posed problems involving monotone operators in infinite dimensional Banach space, when perturbative operators are non ‐ monotone, basing on minimization of norm in interpolation space over closed and convex s

ISSN:0025-584X    

DOI:10.1002/mana.19951730105

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19951730106

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractLetXbe a Banach space. A subspaceLofXis called an operator range if there exists a continuous linear operatorTdefined on some Banach spaceYand such thatTY = L. IfY = XthenLis called an endomorphism range. The paper investigates operator ranges under the following perspectives: (1) Existence (Section 3), (2) Inclusion (Section 4), and (3) Decomposition (Section 5).Section 3 considers the existence inXof operator ranges satisfying certain conditions. The main result is the following: ifXand Fare separable Banach spaces andT : Y →X is a continuous operator with nonclosed range, then there exists a nuclear operatorR:Y→Xsuch thatT + Ris injective and has nonclosed dense range (Theorem 3.2).Section 4 seeks to determine conditions under which every nonclosed operator range in a Banach space is contained in the range of some injective endomorphism with nonclosed dense range. Theorem 4.3 contains a sufficient condition for this. Examples of spaces satisfying this condition are c0,lp(1

ISSN:0025-584X    

DOI:10.1002/mana.19951730107

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractWe present a discrete characterization of Besov and Triebel spaces which is used to determine various classes Fourier multipliers for these spaces. In particular, results of R. Johnson are recovered.

ISSN:0025-584X    

DOI:10.1002/mana.19951730108

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractThe nonlinear eigenvalue problem forp‐Laplacian\documentclass{article}\pagestyle{empty}\begin{document}$$ - div(a(x)|\nabla u|^{p - 2} \nabla u) = \lambda f(x,u) x \in IR^N \lambda >0, $$\end{document}\documentclass{article}\pagestyle{empty}\begin{document}$$ u >0 in IR, \mathop {\lim u = }\limits_{|x| \to \infty } 0, $$\end{document}is considered. We assume that 1

ISSN:0025-584X    

DOI:10.1002/mana.19951730109

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19951730110

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY

摘要:

AbstractLetH(ID) denote the set of analytic functions in the unit disk ID of the complex plane, endowed with the topology of uniform convergence on compact subsets of ID. Let Λ denote the space of continuous linear functionals overH(ID). In this paper we obtain a characterization of those λ ∈Λ such that\documentclass{article}\pagestyle{empty}\begin{document} $ \lambda (z^k B(z)) = 0 for k = 0,1,2,\ldots, $\end{document}whereBis a fixed function inH(ID). We also include a discussion of the sharpness of this characterization and an application to some extremal problem concerni

ISSN:0025-584X    

DOI:10.1002/mana.19951730111

出版商:WILEY‐VCH Verlag    

年代:1995

数据来源: WILEY