共查询到20条相似文献,搜索用时 11 毫秒
1.
We investigate the skew-adjoint extensions of a partial derivative operator acting in the direction of one of the sides a unit square. We investigate the unitary equivalence of such extensions and the spectra of such extensions. It follows from our results, that such extensions need not have discete spectrum. We apply our techniques to the problem of finding commuting skew-adjoint extensions of the partial derivative operators acting in the directions of the sides of the unit square. While our results are most easily stated for the unit square, they are established for a larger class of domains, including certain fractal domains. 相似文献
2.
In this paper we construct a symbol calculus for Banach algebras generated by two idempotents and a coefficient algebra. This, combined with local principles for ?embedding algebras”?, leads to a symbol calculus for singular integral operators on spaces with Muckenhoupt weight and for singular integral operators with measurable coefficients. 相似文献
3.
4.
S.V. Ludkowski 《Advances in Applied Clifford Algebras》2014,24(1):163-178
Families of quasi-permutable normal operators in octonion Hilbert spaces are investigated. Their spectra are studied. Multiparameter semigroups of such operators are considered. A non-associative analog of Stone’s theorem is proved. 相似文献
5.
首先研究了自共轭算子束L—λV的谱曲线,其中L和V是Hilbert空间H内的自共轭算子.其次研究了谱问题Ly=λVy的特征值.最后,将所得的结论应用到正则和奇异的常微分算子的不定谱问题中. 相似文献
6.
In certain circumstances, the uncertainty, ΔS[φ], of a quantum observable, S, can be bounded from below by a finite overall constant ΔS>0, i.e., ΔS[φ]≥ΔS, for all physical states φ. For example, a finite lower bound to the resolution of distances has been used to model a natural ultraviolet cutoff at
the Planck or string scale. In general, the minimum uncertainty of an observable can depend on the expectation value, t=〈φ,S
φ〉, through a function ΔS
t
of t, i.e., ΔS[φ]≥ΔS
t
, for all physical states φ with 〈φ,S
φ〉=t. An observable whose uncertainty is finitely bounded from below is necessarily described by an operator that is merely symmetric
rather than self-adjoint on the physical domain. Nevertheless, on larger domains, the operator possesses a family of self-adjoint
extensions. Here, we prove results on the relationship between the spacing of the eigenvalues of these self-adjoint extensions
and the function ΔS
t
. We also discuss potential applications in quantum and classical information theory.
相似文献
7.
Sergey V. Ludkowski 《Advances in Applied Clifford Algebras》2013,23(3):701-739
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated. 相似文献
8.
9.
M. P. H. Wolff 《Journal of Approximation Theory》2001,113(2):229
Let E be a Banach space over
and let the densely defined closed linear operator A:
(A)E→E be discretely approximated by the sequence ((An,
(An)))n
of operators An where each An is densely defined in the Banach space Fn. Let σa(A) be the approximate point spectrum of A and let σ(An) denote the -pseudospectrum of An. Generalizing our own result, we show that σa(A)lim inf σ(An)=n
∩kn σ(Ak) holds for every >0. We deduce that then for every compact set K
limn dist(σa(A)∩K, σa(An))=0 provided there exists M>0 such that (λ−An)−1M dist(λ, σ(An))−1 holds for every n and every λ in the resolvent set ρ(An) of An. We finally treat the problem under which conditions σa(A) can be approximated from below. More precisely we investigate the problem: Under which assumptions does ∩>0 ∩n
kn σ, a(Ak)σa(A) hold where σ, a(A) denotes the -approximate pseudospectrum? 相似文献
10.
M. I. Gil’ 《Monatshefte für Mathematik》2000,129(1):15-24
Matrix integral operators are considered. Bounds for the spectrum are established. In particular, they give the invertibility
conditions and estimates for the spectral radius.
(Received 16 December 1998; in revised form 30 May 1999) 相似文献
11.
Mediterranean Journal of Mathematics - In this paper we investigate the relationship between some spectra originating from Fredholm theory of a Drazin invertible operator and its Drazin inverse, if... 相似文献
12.
In this paper the essential spectra of closed, densely defined linear operators is characterized on a Banach spaces under
perturbations of n-strictly power compact operators. Further we apply the obtained results to investigate the essential spectra of one-dimensional
transport equation with general boundary conditions and the essential spectra of singular neutron transport equations in bounded
geometries. 相似文献
13.
R. Levy 《Integral Equations and Operator Theory》2007,59(1):35-51
In the paper the local structure of the Fredholm joint spectrum of commuting n-tuples of operators is considered. A connection between the spatial characteristics of operators and the algebraic invariants
of the corresponding coherent sheaves is investigated. A new notion of Weyl joint spectrum of commuting n-tuple is introduced. 相似文献
14.
Sobhy El-Sayed Ibrahim 《Czechoslovak Mathematical Journal》2004,54(1):9-29
In this paper, the general ordinary quasi-differential expression M
pof n-th order with complex coefficients and its formal adjoint M
p
+
on any finite number of intervals I
p
=(a
p
,b
p
),p= 1,...,N, are considered in the setting of the direct sums of L
wp
2
(a
p
,b
p
)-spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations of those in a symmetric case in [1], [14], [15], [16], [17] and of a general case with one interval in [2], [11], [12], whilst others are new. 相似文献
15.
We consider optimal recovery problems in weighted Bergman spaces in the unit ball of ? k . It is shown that if corresponding measures are Carleson and not compactly supported, the optimal recovery algorithm is a limit of optimal recovery algorithms corresponding to truncated problems with compactly supported measures. We also express the Lagrange equation for the dual problem in terms of joint spectra of Toeplitz operators induced by information measures and use this expression for proving that the regularity condition in the dual problem is stable. Examples in the last section illustrate our results. 相似文献
16.
Abstract From both the theoretical and numerical viewpoints, we study a system of differential inclusions describing the evolution of the temperature and the specific humidity distributions in a system of moist air. We allow the so-called saturation concentration parameter to depend on the temperature, and thus we consider more general and interesting phase-change effects than the ones addressed in [2]. 相似文献
17.
It is shown that, for any 1 n < , there exist four maps of the n-dimensional cube to itself such that the limit of any inverse sequence of n-cubes is the limit of some sequence with only these four bonding maps. A universal continuum in the class of all limits of sequences of n-cubes is constructed as the limit of an inverse sequence of n-cubes with one bonding map. All compact sets of trivial shape are represented by using only three maps of the Hilbert cube to itself. Two maps of the closed interval to itself such that any Knaster continuum can be obtained as the limit of an inverse sequence with only these two bonding maps are constructed. 相似文献
18.
We consider the Ising model with external field h and coupling constant J on an infinite connected graph G with uniformly bounded degree. We prove that if G is nonamenable, then the Ising model exhibits phase transition for some h0 and some J<. On the other hand, if G is amenable and quasi-transitive, then phase transition cannot occur for h0. In particular, a group is nonamenable if and only if the Ising model on one (all) of its Cayley graphs exhibits a phase transition for some h0 and some J<. 相似文献
19.
Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils
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In this article we are interested in the numerical computation of spectra of
non-self adjoint quadratic operators. This leads to solve nonlinear eigenvalue problems. We begin with a review of theoretical results for the spectra of quadratic operators, especially for the Schrödinger pencils. Then we present the numerical methods developed to compute the spectra: spectral methods and finite difference discretization, in infinite or in bounded domains. The numerical results obtained are analyzed
and compared with the theoretical results. The main difficulty here is that we have to
compute eigenvalues of strongly non-self-adjoint operators which are very unstable. 相似文献
20.
We discuss the optimality of a sufficient condition from [12] for a point to belong to the essential spectrum of a Toeplitz
operator with a bounded measurable coefficient. Our approach is based on a new sufficient condition for a composition of a
Muckenhoupt weight with a Blaschke product to belong to the same Muckenhoupt class.
The first author was partially supported by CONACYT project U46936-F, Mexico. 相似文献