One-sided invertibility of discrete operators with bounded coefficients

Aequationes mathematicae - For $$p\in (1,\infty )$$ , we establish several criteria of one-sided invertibility on spaces $$l^p=l^p(\mathbb {Z})$$ for discrete band-dominated operators being either...     

Effect of thermal excitations of the reservoir on phase bistability in the fundamental model of quantum optics

The effect of the finite temperature of the reservoir on the phase bistability in the fundamental model of quantum optics is studied based on the Q distribution function calculated numerically and on the P distribution function obtained analytically in the case of large Rabi frequencies. The condition for the appearance of the phase bistability in a system with allowance for thermal excitations of the reservoir is obtained.     

One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces

Let be an oriented Jordan smooth curve and a diffeomorphism of onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertibility of the binomial functional operator

Toeplitz Operators with Semi-Almost-Periodic Matrix Symbols on Hardy Spaces

We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces H ^p (1<p<). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p=2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol.     

Sufficient Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

Suppose α is an orientation preserving diffeomorphism (shift) of \mathbbR₊=(0,￥){{\mathbb{R}}_+=(0,\infty)} onto itself with the only fixed points 0 and ∞. We establish sufficient conditions for the Fredholmness of the singular integral operator with shift

An Algebra of Pseudodifferential Operators with Slowly Oscillating Symbols

Let VR denote the Banach algebra of absolutely continuous functionsof bounded total variation on R, and let B_p be the Banach algebraof bounded linear operators acting on the Lebesgue space L^pRfor 1 < p < . We study the Banach algebra A B_p generatedby the pseudodifferential operators of zero order with slowlyoscillating VR-valued symbols on R. Boundedness and compactnessconditions for pseudodifferential operators with symbols inL R, VR are obtained. A symbol calculus for the non-closed algebraof pseudodifferential operators with slowly oscillating VR-valuedsymbols is constructed on the basis of an appropriate approximationof symbols by infinitely differentiable ones and by use of thetechniques of oscillatory integrals. As a result, the quotientBanach algebra A = A K, where K is the ideal of compact operatorsin B_p, is commutative and involutive. An isomorphism betweenthe quotient Banach algebra A of pseudodifferential operatorsand the Banach algebra of their Fredholm symbols is established. A Fredholm criterionand an index formula for the pseudodifferential operators A A are obtained in terms of their Fredholm symbols. 2000 MathematicsSubject Classification 47G30, 47L15 (primary), 47A53, 47G10(secondary).