Many weighted polynomial inequalities, such as the Bernstein, Marcinkiewicz, Schur, Remez, Nikolskii inequalities, with doubling weights were proved by Mastroianni and Totik for the case [Formula: see text], and by Tamás Erdélyi for [Formula: see text]. In this paper we extend such polynomial inequalities to those for generalized trigonometric polynomials. We also prove the large sieve for gene...

This paper addresses a dynamic feedback stabilization of an interconnected pendulum system with a memory type heat equation, where the kernel memory is an exponential polynomial. By introducing some new variables, the time-variant system is transformed into a time-invariant one. The detailed spectral analysis is presented. Remarkably, the resolvent of the closed-loop system operator is not comp...

This paper considers a computational approach to obtain a reduced order model for polynomial nonlinear systems. The approach is based on balancing generalized gramians of polynomial systems and truncating the systems based on the balanced generalized gramians. The approach utilizes sum of squares programming for its computational purposes.

In this paper, a system level behavioural model for RF power amplifier, which exhibits memory effects, and based on multibranch system is proposed. When higher order terms are included, the memory polynomial model (MPM) exhibits numerical instabilities. A set of memory orthogonal polynomial model (OMPM) is introduced to alleviate the numerical instability problem associated to MPM model. A data...