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Book
Local Fractional Functional Analysis and Its Applications
(2011)
  • Yang Xiao-Jun
Abstract

Local fractional functional analysis is a totally new area of mathematics, and a totally new mathematical world view as well. In this book, a new approach to functional analysis on fractal spaces, which can be used to interpret fractal mathematics and fractal engineering, is presented. From Cantor sets to fractional sets, real line number and the spaces of local fractional functions are derived. Local fractional calculus of real and complex variables is systematically elucidated. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach's spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental introduction to the Yang-Fourier transform, the Yang-Laplace transform, the local fractional short time transform and the local fractional continuous wavelet transform is presented based on the generalized fractal spaces.

Keywords
  • local fractional calculus,
  • local fractional functional analysis,
  • fractal,
  • integral transforms
Publication Date
2011
Editor
Ji-Huan He
Publisher
Asian Academic publisher Limited
ISBN
978-988-19132-1-0
Publisher Statement
This book is coprighted by the publisher
Citation Information
X. Yang . Local Fractional Functional Analysis and Its Applications. Hong Kong: Asian Academic publisher Limited, 2011.