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BIBTEX RIS

On Generalized Harmonic Analysis

1980; American Mathematical Society; Volume: 259; Issue: 1 Linguagem: Inglês

10.2307/1998145

ISSN

1088-6850

Autores

Ka‐Sing Lau, Jonathan Lee,

Tópico(s)

Structural Health Monitoring Techniques

Resumo

Motivated by Wiener's work on generalized harmonic analysis, we consider the Marcinkiewicz space €Hy(R) of functions of bounded upper average/) power and the space 'ViR) of functions of bounded upper p variation.By identifying functions whose difference has norm zero, we show that ^(R), 1 <p < oo, is a Banach space.The proof depends on the result that each equivalence class in ^(R) contains a representative in LP(R).This result, in turn, is based on Masani's work on helixes in Banach spaces.Wiener defined an integrated Fourier transformation and proved that this transformation is an isometry from the nonlinear subspace ^(R) of oo II J-t a-»o+ In J-oo Now, for all/ G L^JR), let 11/11 = 11/11«?= ^[if J ri/(*)i <**) o-2)

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