Almost-Periodic Functions and Functional Equations

ISBN-13: 9781475712568 / Angielski / Miękka / 2013 / 184 str.

L. Amerio; G. Prouse

Opis

The theory of almost-periodic functions with complex values, created by H. Bohr 1] in his two classical papers published in Acta Mathematica in 1925 and 1926, has been developed by many authors and has had note- worthy applications: we recall the works of Weyl, De la Vallee Poussin, Bochner, Stepanov, Wiener, Besicovic, Favard, Delsarte, Maak, Bogoliu- bov, Levitan. This subject has been widely treated in the monographs by Bohr 2], Favard 1], Besicovic 1], Maak 1], Levitan 1], Cinquini 1], Corduneanu 1], 2]. An important class of almost-periodic functions was studied at the beginning of the century by Bohl and Esclangon. Bohr's theory has been extended by Muckenhoupt 1] in a particular case and, subsequently, by Bochner 1] and by Bochner and Von Neumann 1] to very general abstract spaces. The extension to Banach spaces is, in particular, of great interest, in view of the fundamental importance of these spaces in theory and application.

Spis treści

Theory of Almost-Periodic Functions.- Almost-Periodic Functions in Banach Spaces.- Harmonic Analysis of Almost-Periodic Functions.- Weakly Almost-Periodic Functions.- The Integration of Almost-Periodic Functions.- Applications to Almost-Periodic Functional Equations.- The Wave Equation.- The Schrödinger Type Equation.- The Wave Equation with Nonlinear Dissipative Term.- Results Regarding other Functional Equations.