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Abbas Najati

Publications and source records attributed to Abbas Najati.

3 recordsLinked to original sources
arXiv2025

Hyers-Ulam Type Stability of the Pexiderized Cauchy Functional Equation in Locally Convex Cones

The foundation of locally convex cone theory relies on order-theoretic concepts that induce specific topological frameworks. Within this structure, cones naturally possess three distinct topologies: lower, upper, and symmetric. In this paper, we consider the Hyers-Ulam type stability of the Pexiderized Cauchy functional equation $f(x+y)=g(x)+h(y)$ in locally convex cones. Additionally, we present several significant corollaries that follow from our primary findings.

math.FA↗
arXiv2019

Dynamical sampling: mixed frame operators, representations and perturbations

Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n φ\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames induced by the action of powers of bounded linear operators. As a particular case, we discuss problems concerning representation of frames in terms of iterations of the mixed frame operators. As our another contribution, we consider frames of the form $ \{a_n T^n φ\}_{n=0}^{\infty} $ for some non-zero scalars $ \{a_n\}_{n=0}^{\infty} $, and we obtain some new results in dynamical sampling. Finally, we will present some auxiliary results related to the perturbation of sequences of the form $ \{T^n φ\}_{n=0}^{\infty}$.

math.FA↗