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Focusing on finite element methods, this book serves as a comprehensive resource for graduate students and researchers in applied mathematics, physics, and engineering. It covers the nodal method for various geometries, explores error estimation between exact and approximate solutions, and addresses the approximation of positive symmetric first-order systems. Additionally, it delves into continuous and discontinuous approximation methods tailored for the transport equation, culminating in linear systems that facilitate practical applications.

Focusing on spectral theory, this volume delves into linear operators on Banach spaces, exploring essential spectra and their generalizations. It offers a thorough survey of significant results related to different types of essential spectra, making it a valuable resource for those studying this advanced mathematical field.

Focusing on spectral theory, this book explores key topics such as the completeness of generalized eigenvectors, Riesz bases, and semigroup theory. It addresses recent advancements in perturbed non-self-adjoint operators, including their eigenvalue behavior and applications in physical problems like sound radiation from vibrating plates. The content is designed for students and researchers in spectral theory, pure analysts, and mathematicians, offering a blend of theoretical insights and practical implications in mathematical physics and mechanics.

This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν -convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T ( ε ) Frame of the perturbed operator T ( ε ) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Focusing on Fredholm operators and spectral theory, this volume rigorously explores recent mathematical advancements, particularly in polynomially-compact operators. It connects abstract concepts to practical applications, emphasizing their significance in the stability of physical systems and various mathematical fields. The text delves into classical Riesz theory, aiming to provide existence results for second kind operator equations, ultimately aiding readers in understanding the spectrum, eigenvalue multiplicities, and localization of these operators.