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11.
M. Amélia Bastos Claudio A. Fernandes Yuri I. Karlovich 《Complex Analysis and Operator Theory》2008,2(2):241-272
The C*-subalgebra of generated by all multiplication operators by slowly oscillating and piecewise continuous functions, by the Cauchy singular
integral operator and by the range of a unitary representation of an amenable group of diffeomorphisms with any nonempty set of common fixed points is studied. A symbol calculus for the C*-algebra and a Fredholm criterion for its elements are obtained. For the C*-algebra composed by all functional operators in , an invertibility criterion for its elements is also established. Both the C*-algebras and are investigated by using a generalization of the local-trajectory method for C*-algebras associated with C*-dynamical systems which is based on the notion of spectral measure.
Submitted: April 30, 2007. Accepted: November 5, 2007. 相似文献
12.
Karlovich Alexei Yu. Karlovich Yuri I. Lebre Amarino B. 《Mediterranean Journal of Mathematics》2016,13(6):4413-4435
Mediterranean Journal of Mathematics - Let $${\alpha}$$ be an orientation-preserving homeomorphism of $${[0,\infty]}$$ onto itself with only two fixed points at 0 and $${\infty}$$ , whose... 相似文献
13.
Let ${\mathcal{B}_{p,w}}$ be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space ${L^{p}(\mathbb{R}, w)}$ , where ${p \in (1, \infty)}$ and w is a Muckenhoupt weight. We study the Banach subalgebra ${\mathfrak{A}_{p,w}}$ of ${\mathcal{B}_{p,w}}$ generated by all multiplication operators aI ( ${a \in PSO^{\diamond}}$ ) and all convolution operators W 0(b) ( ${b \in PSO_{p,w}^{\diamond}}$ ), where ${PSO^{\diamond} \subset L^{\infty}(\mathbb{R})}$ and ${PSO_{p,w}^{\diamond} \subset M_{p,w}}$ are algebras of piecewise slowly oscillating functions that admit piecewise slowly oscillating discontinuities at arbitrary points of ${\mathbb{R} \cup \{\infty\}}$ , and M p,w is the Banach algebra of Fourier multipliers on ${L^{p}(\mathbb{R}, w)}$ . Under some conditions on the Muckenhoupt weight w, we construct a Fredholm symbol calculus for the Banach algebra ${\mathfrak{A}_{p,w}}$ and establish a Fredholm criterion for the operators ${A \in \mathfrak{A}_{p,w}}$ in terms of their Fredholm symbols. To study the Banach algebra ${\mathfrak{A}_{p,w}}$ we apply the theory of Mellin pseudodifferential operators, the Allan–Douglas local principle, the two idempotents theorem and the method of limit operators. The paper is divided in two parts. The first part deals with the local study of ${\mathfrak{A}_{p,w}}$ and necessary tools for studying local algebras. 相似文献
14.
J. A. Ball Yu. I. Karlovich L. Rodman I. M. Spitkovsky 《Integral Equations and Operator Theory》1998,32(3):243-281
Sarason interpolation and Toeplitz corona problems are studied for almost periodic matrix functions. Recent results on almost periodic factorization and related generalized Toeplitz operators are the main tools in the study.Supported in part by NSF Grant DMS 9500912Supported in part by NATO Collaborative Research Grant 950332Supported by NSF Grant DMS 9500924 相似文献
15.
A. Yu. Karlovich 《Mathematical Notes》1996,64(3):330-341
We consider the Banach algebra $\mathfrak{A}$ of singular integral operators with matrix piecewise continuous coefficients in the reflexive Orlicz spaceL M n (Γ). We assume that Γ belongs to a certain wide subclass of the class of Carleson curves; this subclass includes curves with cusps, as well as curves of the logarithmic spiral type. We obtain an index formula for an arbitrary operator from the algebra $L_M^n (\Gamma )$ in terms of the symbol of this operator. 相似文献
16.
Albrecht Bö ttcher Yuri I. Karlovich 《Transactions of the American Mathematical Society》1999,351(8):3143-3196
We describe the spectra and essential spectra of Toeplitz operators with piecewise continuous symbols on the Hardy space in case , is a Carleson Jordan curve and is a Muckenhoupt weight in . Classical results tell us that the essential spectrum of the operator is obtained from the essential range of the symbol by filling in line segments or circular arcs between the endpoints of the jumps if both the curve and the weight are sufficiently nice. Only recently it was discovered by Spitkovsky that these line segments or circular arcs metamorphose into horns if the curve is nice and is an arbitrary Muckenhoupt weight, while the authors observed that certain special so-called logarithmic leaves emerge in the case of arbitrary Carleson curves with nice weights. In this paper we show that for general Carleson curves and general Muckenhoupt weights the sets in question are logarithmic leaves with a halo, and we present final results concerning the shape of the halo.
17.
18.
In this paper we study the Banach algebra of singular integral operators with piecewise continuous coefficients and a Carleman orientation-reversing slowly oscillating shift on the Lebesgue space with a power weight on the unit circle. The slow oscillation of the shift derivative, in contrast to the classic assumption on its piecewise continuity, leads to the appearance of massive local spectra for the considered operators. Applying localization techniques and the theory of Mellin pseudodifferential and associated limit operators, we construct a symbol calculus for the above-mentioned operator algebra and find a Fredholm criterion and an index formula for the operators in this algebra in terms of their symbols.Partially supported by CONaCYT grant, Cátedra Patrimonial, No. 990017-EX and by CONACYT project 32726-E, México.Partially supported by F. C. T. grant Praxis XXI/2/2.1/MAT/441/94, Portugal. 相似文献
19.
Bastos M. A.; Karlovich Yu. I.; Silbermann B. 《Proceedings London Mathematical Society》2004,89(3):697-737
We develop the Fredholm theory for Toeplitz operators, withsymbols in the C*-algebra D = [SO, SAP]n, n generated by allslowly oscillating (SO) and semi-almost periodic (SAP) n x nmatrix functions, on the Hardy spaces (with 1 < p < ) over the upper half-plane.Using limit operator techniques, we get necessary Fredholm conditionsfor any operator in the Banach algebra alg(S, D) of singularintegral operators with coefficients in D on the space [Lp (R)]n.Applying the AllanDouglas local principle and the theoryof Toeplitz operators with SAP matrix symbols, we also establishFredholm criteria for Toeplitz operators with matrix symbolsg D on the space . An index formula for Fredholm Toeplitz operators with matrix symbolsin D is obtained on the basis of an appropriate approximationof slowly oscillating components of the symbols. 2000 MathematicsSubject Classification 47B35 (primary), 47A53 (secondary). 相似文献
20.
The effect of thermal photons on the radiative properties of a one-atom maser is investigated. Stationary Pand Qdistribution functions are determined analytically in the approximation of strong interaction between an atom and a cavity field mode. The generation conditions are found for a one-atom maser. It is shown that taking into account thermal photons leads to a decrease in the threshold value of incoherent pumping. It is demonstrated that generation may occur in the absence of population inversion in the atomic subsystem and when losses exceed the intensity of incoherent pumping. A formula is proposed for the Fano factor of a one-atom maser in the form of the sum of the Fano factors of the microcavity radiation in the absence of thermal photons and the thermal radiation. 相似文献