Difference Spaces and Invariant Linear Forms

1994
ISBN: 978-3-540-58323-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1586, 192 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 318 g

Reihe: Lecture Notes in Mathematics

Difference spaces arise by taking sums of finite or fractional differences. Linear forms which vanish identically on such a space are invariant in a corresponding sense. The difference spaces of L2 (Rn) are Hilbert spaces whose functions are characterized by the behaviour of their Fourier transforms near, e.g., the origin. One aim is to establish connections between these spaces and differential operators, singular integral operators and wavelets. Another aim is to discuss aspects of these ideas which emphasise invariant linear forms on locally compact groups. The work primarily presents new results, but does so from a clear, accessible and unified viewpoint, which emphasises connections with related work.

Zielgruppe

Research

Autoren/Hrsg.

Nillsen, Rodney

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

General and preparatory results.- Multiplication and difference spaces on R n.- Applications to differential and singular integral operators.- Results for L p spaces on general groups.