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The Integration of Almost-Periodic Functions

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Part of the The University Series in Higher Mathematics book series (USHM)

Abstract

Let X be a Banach space and x= f(t) a continuous function from J to X. We shall set

EquationSource% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaabm % aabaGaamiDaaGaayjkaiaawMcaaiabg2da9maapehabaGaamOzaiaa % cIcacqaH3oaAcaGGPaGaamizaiabeE7aObWcbaGaaGimaaqaaiaads % haa0Gaey4kIipaaaa!44E6! \[F\left( t \right) = \int\limits_0^t {f(\eta )d\eta } \]$$
((1.1))

Keywords

  • Banach Space
  • Uniform Convergence
  • Inverse Fourier Transform
  • Fourier Expansion
  • Bounded Sequence

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1971 Springer Science+Business Media New York

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Amerio, L., Prouse, G. (1971). The Integration of Almost-Periodic Functions. In: Almost-Periodic Functions and Functional Equations. The University Series in Higher Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1254-4_4

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  • DOI: https://doi.org/10.1007/978-1-4757-1254-4_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-1256-8

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