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1.
On the level sets of the resolvent norm of a linear operator 总被引:1,自引:0,他引:1
We construct a bounded linear operator on a Banach space anda closed densely defined operator on a Hilbert space with resolventnorms that are constant in a neighbourhood of zero. We alsodiscuss cases where the norm of the resolvent of a bounded linearoperator cannot be constant on an open set. 相似文献
2.
We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space with the resolvent norm
that is constant in a neighbourhood of zero.
相似文献
3.
Eugene Shargorodsky 《Archive for Rational Mechanics and Analysis》2013,209(1):41-59
Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two-dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler–Lagrange equation of a certain functional; this allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result. 相似文献
4.
In the first part [1] of the paper the basic boundary value problems of the mathematical theory of elasticity for three-dimensional anisotropic bodies with cuts were formulated. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems were formulated in the Besov
and Bessel-potential (
p
s
) spaces. In the present part we give the proofs of the main results (Theorems 7 and 8) using the classical potential theory and the nonclassical theory of pseudodifferential equations on manifolds with a boundary. 相似文献
5.
We continue the study of algebras generated by the Cauchy singular integral operator and integral operators with fixed singularities on the unit interval, started in R.Duduchava, E.Shargorodsky, 1990. Such algebras emerge when one considers singular integral operators with complex conjugation on curves with cusps. As one of possible applications of the obtained results we find an explicit formula for the local norms of the Cauchy singular integral operator on the Lebesgue spaceL
2
(, ), where is a curve with cusps of arbitrary order and is a power weight. For curves with angles and cusps of order 1 the formula was already known (see R.Avedanio, N.Krupnik, 1988 and R.Duduchava, N.Krupnik, 1995).
Dedicated to Professor
Israel Gohberg
on the occasion of his 70-th birthday
Supported by EPSRC grant GR/K01001 相似文献
6.
We consider the phenomenon of spectral pollution arising incalculation of spectra of self-adjoint operators by projectionmethods. We suggest a strategy of dealing with spectral pollutionby using the so-called second-order relative spectra. The effectivenessof the method is illustrated by a detailed analysis of two modelexamples. 相似文献
7.
The three-dimensional problems of the mathematical theory of thermoelasticity are considered for homogeneous anisotropic bodies with cuts. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems of statics and pseudo-oscillations are proved in the Besov (
) and Bessel-potential (
) spaces by means of the classical potential methods and the theory of pseudodifferential equations on manifolds with boundary. Using the embedding theorems, it is proved that the solutions of the considered problems are Hölder continuous. It is shown that the displacement vector and the temperature distribution function areC
-regular with any exponent <1/2.This paper consists of two parts. In this part all the principal results are formulated. The forthcoming second part will deal with the auxiliary results and proofs. 相似文献
8.
We study spectral properties of second-order elliptic operators with periodic coefficients in dimension two. These operators
act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition. The main
result is the absolute continuity of the spectra of such operators. The cornerstone of the proof is an isothermal change of
variables, reducing the metric to a flat one and the waveguide to a straight strip. The main technical tool is the quasiconformal
variant of the Riemann mapping theorem.
This work is supported by The Royal Society. 相似文献
9.
E. Shargorodsky 《Journal of Functional Analysis》2003,197(1):283-300
Motivated by a question from mathematical hydrodynamics, this paper studies the solution set of Riemann-Hilbert problems on the unit disc D in of the form
10.
Eugene Shargorodsky 《Integral Equations and Operator Theory》2007,57(1):127-132
We establish a sufficient condition for a point to belong to the essential spectrum of a Toeplitz operator with a bounded
measurable coefficient. This condition uses geometric information on the cluster values of the coefficient. 相似文献