Investigation of orthogonal systems: trigonometric, Walsh, Vilenkin, rational systems.  Analizing convergence and divergence properties. Construction of integrability and L_1 convergence classes. Strong summation, approximation. Studying the boundedness of multiplier operators in various Banach spaces. Investigation of Hardy spaces in different settings.   

Developing adaptive methods that are adjusted to the specific types of signals, images and the concrete task in time, space and frequency domains. Processing of biomedical signals: ECG, EEG, blood pressure. Feature extraction for classification and compressing. Detection of anomalies.  Research and application of variable orthogonal projections.