摘要:

AbstractThe point spectrum lying on the essential spectrum is investigated for the one‐dimensional Schrödinger operator\documentclass{article}\pagestyle{empty}\begin{document}$ \- \frac{{d^2 }}{{dx^2 }} + q(x) $\end{document}with decaying potentialq, and weakly perturbed Stark‐like operator\documentclass{article}\pagestyle{empty}\begin{document}$ - \frac{{d^2 }}{{dx^2 }} - \left| x \right|^\alpha {\rm sign }x + q(x). $\end{document}An elementary constructive technique is developed to obtain various results concerning embedded eigenvalues of Schrödinger operators. In Section 3 a constructive example of the Stark ‐ like operator with the potentialqdecaying slightly slowlier than o(1/|x|1‐α/2)and dense point spectrum on the whole real axis is

ISSN:0025-584X    

DOI:10.1002/mana.19971830112

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractWe study semilinear problems in which the nonlinear part is linear at infinity but behaves like a function intersecting many of the eigenvalues of the linear operator. The asymptotic linear operator can have a null space of any finite dimension.

ISSN:0025-584X    

DOI:10.1002/mana.19971830113

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractIn this paper we introduce the notion of pseudo ‐ergodicity to generalize Pustyl'nikov's estimates of Weyl sums to Weyl sums over subsequence of the natural number

ISSN:0025-584X    

DOI:10.1002/mana.19971830114

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractSome methods are described for reducing the problem of the boundedness of pseudodifferential operators (ΨDOs) to the theory of Fourier multipliers. Special attention is given to the boundedness of ΨDOs in Besov ‐ Triebel ‐ Lizorkin s

ISSN:0025-584X    

DOI:10.1002/mana.19971830115

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractThe absolutely continuous and singular spectrum of one‐dimensional Schrödinger operators with slowly oscillating potentials and perturbed periodic potentials is studied, continuing similar investigations for Jacobi matrices from [14]. Trace class methods are used to locate the singular spectrum. The absolutely continuous spectrum is determined by iterated diagonalization of transfer matrices to prove boundedness of eigensolutio

ISSN:0025-584X    

DOI:10.1002/mana.19971830116

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractAn ordinary differential equation of the typewith parameterξ ϵ IRnand smooth coefficients aj,aϵC∞([‐T,T]) is studied. It is assumed that all the characteristic roots of the equation vanish att= 0 while fort≠ 0 they are real and distinct. The constructions of real‐valued phase functions ϕpHkl(k,l= 1., m) and of amplitude functionsAjklsuch that for a givens ϵ[‐T, T] every solutionu(t, ξ) of the equation can be represented aswhere Ψj(s, ξ)= Djtu(s,ξ), j

ISSN:0025-584X    

DOI:10.1002/mana.19971830117

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19971830101

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY