Open AccessREPRESENTATION OF PARSEVAL FRAMES IN HILBERT SPACES
Author(s) -
Igor Sergeevich Ryabtsov
Publication year - 2011
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2011-17-5-60-70
Subject(s) - parseval's theorem , orthonormal basis , mathematics , simple (philosophy) , representation (politics) , hilbert space , dimension (graph theory) , pure mathematics , basis (linear algebra) , algebra over a field , mathematical analysis , fourier transform , fourier analysis , geometry , physics , politics , political science , fractional fourier transform , law , philosophy , epistemology , quantum mechanics
In this paper we introduce two new classes of Parseval frames in arbitraryHilbert spaces of finite or infinite dimension: simple and composite Parsevalframes. Theorems of representation of composite Parseval frames by summationof simple ones are proved. Few classes of simple frames are described: orthonormal basis, equiangular Parseval frames and some other examples.