Spectra of Ruelle Transfer Operators for Contact Flows

In this survey article we discuss some recent results concerning strong spectral estimates for Ruelle transfer operators for contact flows on basic sets similar to these of Dolgopyat obtained in the case of Anosov flows with C1 stable and unstable foliations. Some applications of Dolgopyat's results and the more recent ones are also described.

Spectral Shift Function for the Perturbations of Schrödinger Operators at High Energy

2000 Mathematics Subject Classification: 35P20, 35J10, 35Q40.

Generalized D-Symmetric Operators I

2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30.

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity

2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10.