The windowed Fourier transform on R

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The windowed Fourier transform on R


Defi nition-Proposition-Theorems (Plancherel formula-Parseval formula-inversion formula-Calderon's formula)

http://www.4shared.com/office/b2Ho5n7H/The_windowed_Fourier_transform.html
 

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A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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