Preliminaries on Crossed Products

Schulz-Baldes H, Stoiber T (2022)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2022

Publisher: Springer

Series: Mathematical Physics Studies

Book Volume: Part F1111

Pages Range: 1-21

DOI: 10.1007/978-3-031-12201-9_1

Abstract

This chapter reviews several facts about crossed products. Many aspects are covered in the standard reference [1], but some are taken from other works like [2–7]. Many results hold for general locally compact abelian group actions, but for sake of concreteness we will only restrict to the case of abelian n-parameter groups which are relevant for the applications that we have in mind. Hence throughout G=Tn0⊕Rn1 where n= n0+ n1 and we make the identification T= R\ Z= [ 0, 1 ] / ∼. Unless there is an explicitly different choice of normalization (which only applies in Chap. 5), we fix the Haar measures on T^d and R^d to be the usual Lebesgue measure and on Z^d the counting measure. Combined with the conventions for the Fourier transform as given below, one can then identify the dual groups T^ = Z, Z^ = T and R^ = R in such a way that the Plancherel theorem holds without proportionality constants.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

How to cite

APA:

Schulz-Baldes, H., & Stoiber, T. (2022). Preliminaries on Crossed Products. In (pp. 1-21). Springer.

MLA:

Schulz-Baldes, Hermann, and Tom Stoiber. "Preliminaries on Crossed Products." Springer, 2022. 1-21.

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