共查询到20条相似文献,搜索用时 515 毫秒
1.
We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators Aj on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators. 相似文献
2.
《Journal of Mathematical Analysis and Applications》1986,114(2):328-339
Integral formulas from the theory of holomorphic functions of several variables are applied to explicit treatment of the analytic functional calculus for commuting operators in Banach spaces (commutative Banach algebras). Among others the integral formula of Henkin in smooth convex domains, is used. An application is also given to commuting normal operators in Hilbert spaces. 相似文献
3.
本文研究了具有有限升标(降标)的半Fredholm算子,证明了具有有限 升标(降标)的上半Fredholm算子在其摄动类中交换元的摄动下仍具有同样性质,对于下半Fredholm算子有同样结论。从而改进了[1,2]中的主要结果。同时,我们证明了被摄动算子集合扩大(相对于[1]而言)而摄动仍为紧摄动时较[1]中更强的结果。 相似文献
4.
Boris Yu. Sternin 《Central European Journal of Mathematics》2011,9(4):814-832
We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class
of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator
acting in sections of infinite-dimensional bundles. 相似文献
5.
V. S. Oganesyan 《Mathematical Notes》2016,99(1-2):308-311
Commuting differential operators of rank 2 are considered. With each pair of commuting operators a complex curve called the spectral curve is associated. The genus of this curve is called the genus of the commuting pair. The dimension of the space of common eigenfunctions is called the rank of the commuting operators. The case of rank 1 was studied by I. M. Krichever; there exist explicit expressions for the coefficients of commuting operators in terms of Riemann theta-functions. The case of rank 2 and genus 1 was considered and studied by S. P. Novikov and I.M. Krichever. All commuting operators of rank 3 and genus 1 were found by O. I. Mokhov. A. E. Mironov invented an effective method for constructing operators of rank 2 and genus greater than 1; by using this method, many diverse examples were constructed. Of special interest are commuting operators with polynomial coefficients, which are closely related to the Jacobian problem and many other problems. Common eigenfunctions of commuting operators with polynomial coefficients and smooth spectral curve are found explicitly in the present paper. This has not been done so far. 相似文献
6.
A. E. Mironov 《Siberian Mathematical Journal》2001,43(1):97-113
We indicate smooth real commuting differential operators whose eigenvalues and eigenfunctions are parametrized by principally polarized abelian varieties. 相似文献
7.
We indicate smooth real commuting differential operators whose eigenvalues and eigenfunctions are parametrized by principally polarized abelian varieties. 相似文献
8.
A. A. Murach 《Ukrainian Mathematical Journal》2007,59(6):874-893
We study linear elliptic pseudodifferential operators in the improved scale of functional Hilbert spaces on a smooth closed manifold. Elements of this scale are isotropic Hörmander-Volevich-Paneyakh spaces. We investigate the local smoothness of a solution of an elliptic equation in the improved scale. We also study elliptic pseudodifferential operators with parameter. 相似文献
9.
Morteza Seddighin 《Journal of Mathematical Analysis and Applications》2005,312(1):61-71
We will study the joint antieigenvalues of pairs of operators that belong to the same closed normal subalgebra of B(H). This extends antieigenvalue theory from single normal operators to pairs of commuting normal operators. 相似文献
10.
In this paper, we introduce the notion of generalized spherical Aluthge transforms for commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) subspaces between the generalized spherical Aluthge transform and the original commuting pair. Next, we study the norm continuity through generalized Aluthge transform maps. We also study how the Taylor spectra and the Fredrolm index of commuting pairs of operators behave under the spherical Duggal transform. Finally, we introduce the notion of Campbell binormality for commuting pairs of operators and investigate some of its basic properties under spherical Aluthge and Duggal transforms. Moreover, we obtain new set inclusion diagrams among normal, quasinormal, centered, and Campbell binormal commuting pairs of operators. 相似文献
11.
Daoxing Xia 《Integral Equations and Operator Theory》1996,24(1):106-125
In this paper, we study the model of a pure subnormal operator with finite rank self-commutator and of the relatedn-tuple of commuting linear bounded operators. We also give some applications of the model to the theory ofn-tuples of commuting operators with trace class self-commutators.This work is supported in part by a NSF grant no. DMS-9400766. 相似文献
12.
本文讨论了Fock空间上以径向函数和拟齐次函数为符号的Toeplitz算子的代数性质,给出了两个以径向函数为符号的Toeplitz算子的积仍为Toeplitz算子的充分必要条件,并且研究了以拟齐次函数为符号的Toeplitz算子的交换性. 相似文献
13.
M.I. Gil' 《Journal of Mathematical Analysis and Applications》2005,308(1):140-158
We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators. 相似文献
14.
Andrey E. Mironov 《Inventiones Mathematicae》2014,197(2):417-431
In this paper we study self-adjoint commuting ordinary differential operators of rank two. We find sufficient conditions when an operator of fourth order commuting with an operator of order 4g+2 is self-adjoint. We introduce an equation on potentials V(x),W(x) of the self-adjoint operator \(L=(\partial_{x}^{2}+V)^{2}+W\) and some additional data. With the help of this equation we find the first example of commuting differential operators of rank two corresponding to a spectral curve of higher genus. These operators have polynomial coefficients and define commutative subalgebras of the first Weyl algebra. 相似文献
15.
In this paper we will reconsider the topological structure of Menger probabilistic normed spaces (briefly PN-spaces) under the t-norm M. We will prove that this topology is compatible with the topology induced by a countable and separating family of semi-norms, and hence the well-known theorems of classical functional analysis (such as the principle of uniform boundedness, open mapping and closed graph theorems) are valid in this context also. We will meanwhile obtain a method by which one may construct easily a large class of PN-spaces. Finally, using this method, we see that a certain subspace of bounded linear operators between PN-spaces, i.e. the class of strongly bounded linear operators, has a natural PN structure. 相似文献
16.
Let R and S be commuting n-tuples of operators. We will give some spectral relations between RS and SR that extend the case of single operators. We connect the Taylor spectrum, the Fredholm spectrum and some other joint spectra of RS and SR. Applications to Aluthge transforms of commuting n-tuples are also provided. 相似文献
17.
Commuting Dual Toeplitz Operators on the Polydisk 总被引:1,自引:0,他引:1
Yu Feng LU Shu Xia SHANG 《数学学报(英文版)》2007,23(5):857-868
On the polydisk, the commutativity of dual Toeplitz operators is studied. We obtain characterizations of commuting dual Toeplitz operators, essentially commuting dual Toeplitz operators and essentially semi-commuting dual Toeplitz operators. 相似文献
18.
We prove that n pairwise commuting derivations of the polynomial ring (or the power series ring) in n variables over a field k of characteristic 0 form a commutative basis of derivations if and only if they are k-linearly independent and have no common Darboux polynomials. This result generalizes a recent result due to Petravchuk and is an analogue of a well-known fact that a set of pairwise commuting linear operators on a finite dimensional vector space over an algebraically closed field has a common eigenvector. 相似文献
19.
We investigate pairs of commuting Foias-Williams/Peller type operators acting on vector-valued weighted Bergman spaces. We prove that a commuting pair of such operators is jointly polynomially bounded if and only if it is similar to a pair of contractions, if and only if both operators are polynomially bounded. 相似文献
20.
《数学物理学报(B辑英文版)》2017,(5)
A closed linear relation T in a Banach space X is called left(resp. right) Fredholm if it is upper(resp. lower) semi Fredholm and its range(resp. null space) is topologically complemented in X. We say that T is left(resp. right) Browder if it is left(resp. right)Fredholm and has a finite ascent(resp. descent). In this paper, we analyze the stability of the left(resp. right) Fredholm and the left(resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered. 相似文献