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3.
Iteration of analytic functions of operators 总被引:3,自引:0,他引:3
Ky Fan 《Mathematische Zeitschrift》1982,179(3):293-298
4.
Wiener-Hopf operators and generalized analytic functions 总被引:1,自引:0,他引:1
An almost periodic generalization of H+C is defined and analyzed. Applications of this analysis are made to the type II index theory of Wiener-Hopf operators with almost periodic symbols.Supported in part by the National Science Foundation. 相似文献
5.
Nak Eun Cho 《Journal of Mathematical Analysis and Applications》2003,286(1):168-176
The purpose of the present paper is to investigate some integral preserving properties for certain analytic functions in the open unit disk. We also obtain the conditions for close-to-convex functions in a sector. Our results contain some interesting corollaries as the special cases. 相似文献
6.
A. K. Kitover 《Journal of Mathematical Sciences》1987,37(5):1353-1357
The spectrum of weighted conformai substitution operators is determined in a large class of Banach spaces of analytic functions, including many spaces whose norm is defined in terms of the properties of the functions themselves and of their derivatives.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 141, pp. 154–161, 1985. 相似文献
7.
Mercedes H. Rosas Bruce E. Sagan 《Transactions of the American Mathematical Society》2006,358(1):215-232
Consider the algebra of formal power series in countably many noncommuting variables over the rationals. The subalgebra of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur symmetric functions as well as investigating their properties.
8.
Konstantin M. Dyakonov 《Mathematische Annalen》2009,344(2):353-380
For a Toeplitz operator T
φ
, we study the interrelationship between smoothness properties of the symbol φ and those of the functions annihilated by T
φ
. For instance, it follows from our results that if φ is a unimodular function on the circle lying in some Lipschitz or Zygmund space Λα with 0 < α < ∞, and if f is an H
p
-function (p ≥ 1) with T
φ
f = 0, then f ∈ Λα and
for some c = c(α, p) and d = d(α, p); an explicit formula for the optimal exponent d is provided. Similar—and more general—results for various smoothness classes are obtained, and several approaches are discussed.
Furthermore, since a given non-null function f ∈ H
p
lies in the kernel of with , we derive information on the smoothness of H
p
-functions with smooth arguments. This can be viewed as a natural counterpart to the existing theory of analytic functions
with smooth moduli.
Supported in part by grants MTM2008-05561-C02-01/MTM, HF2006-0211 and MTM2007-30904-E from El Ministerio de Ciencia e Innovación
(Spain), and by grant 2005-SGR-00611 from DURSI (Generalitat de Catalunya). 相似文献
9.
Let Ω be a simply connected domain in the complex plane, and , the space of functions which are defined and analytic on , if K is the operator on elements defined in terms of the kernels ki(t, s, a1, …, an) in by is the identity operator on , then the operator I ? K may be factored in the form (I ? K)(M ? W) = (I ? ΠK)(M ? ΠW). Here, W is an operator on defined in terms of a kernel w(t, s, a1, …, an) in by Wu = ∝antw(t, s, a1, …, an) u(s, a1, …, an) ds. ΠW is the operator; ΠWu = ∝an ? 1w(t, s, a1, …, an) u(s, a1, …, an) ds. ΠK is the operator; ΠKu = ∑i = 1n ? 1 ∝aitki(t, s, a1, …, an) ds + ∝an ? 1tkn(t, s, a1, …, an) u(s, a1, …, an) ds. The operator M is of the form m(t, a1, …, an)I, where and maps elements of into itself by multiplication. The function m is uniquely derived from K in the following manner. The operator K defines an operator on functions u in , by . A determinant of the operator is defined as an element of . This is mapped into by setting an + 1 = t to give m(t, a1, …, an). The operator I ? ΠK may be factored in similar fashion, giving rise to a chain factorization of I ? K. In some cases all the matrix kernels ki defining K are separable in the sense that ki(t, s, a1, …, an) = Pi(t, a1, …, an) Qi(s, a1, …, an), where Pi is a 1 × pi matrix and Qi is a pi × 1 matrix, each with elements in , explicit formulas are given for the kernels of the factors W. The various results are stated in a form allowing immediate extension to the vector-matrix case. 相似文献
10.
LetM be a von Neumann algebra with a faithful normal tracial state and letH
be a finite maximal subdiagonal subalgebra ofM. LetH
2 be the closure ofH
in the noncommutative Lebesgue spaceL
2(M). We consider Toeplitz operators onH
2 whose symbol belong toM, and find that they possess several of the properties of Toeplitz operators onH
2(
) with symbol fromL
(
), including norm estimates, a Hartman-Wintner spectral inclusion theorem, and a characterisation of the weak* continuous linear functionals on the space of Toeplitz operators. 相似文献
11.
Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lp spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on Hinfin functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions. 相似文献
12.
Sofiya Ostrovska 《Proceedings Mathematical Sciences》2007,117(4):485-493
Let φ be a power series with positive Taylor coefficients {a
k
}
k=0∞ and non-zero radius of convergence r ≤ ∞. Let ξ
x
, 0 ≤ x < r be a random variable whose values α
k
, k = 0, 1, …, are independent of x and taken with probabilities a
k
x
k
/φ(x), k = 0, 1, ….
The positive linear operator (A
φ
f)(x):= E[f(ξ
x
)] is studied. It is proved that if E(ξ
x
) = x, E(ξ
x
2) = qx
2 + bx + c, q, b, c ∈ R, q > 0, then A
φ
reduces to the Szász-Mirakyan operator in the case q = 1, to the limit q-Bernstein operator in the case 0 < q < 1, and to a modification of the Lupaş operator in the case q > 1. 相似文献
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John W Bunce 《Journal of Functional Analysis》1984,57(1):21-30
This paper proves versions of the Rota model theorem, the de Branges-Rovnyak model theorem, and the coisometric extension theorem for n-tuples of not necessarily commuting operators. This generalizes the work of A. E. Frazho (J. Funct. Anal.48 (1982), 1–11) for pairs of operators. The methods involve applying the single operator results to matrices of operators. 相似文献
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16.
《Quaestiones Mathematicae》2013,36(3):411-419
Abstract We study the existence and the continuity of superposition operators between weighted spaces of holomorphic functions in terms of the weights. 相似文献
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Arthur E Frazho 《Journal of Functional Analysis》1984,59(3):445-461
This paper develops a dilation theory for two noncommutative operators. Many of the results and techniques in dilation theory for one operator are extended to this setting. This is done by extending the Schaffer construction for one operator to the Fock space setting. A new Wold decomposition for two isometrics with orthogonal range is obtained. This Wold decomposition and the Schaffer construction is used to extend the Sz.-Nagy-Foias lifting theorem and the characteristic function theory to the noncommutative setting. The characteristic function is operator valued and defined in a Fock space. 相似文献
19.
B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献