TY - CHAP

T1 - On multiplicative maps of continuous and smooth functions

AU - Artstein-Avidan, Shiri

AU - Faifman, Dmitry

AU - Milman, Vitali

PY - 2012

Y1 - 2012

N2 - In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a diffeomorphism of the underlying manifold (with a bit more freedom in families of continuous functions). Our results in the real case are mostly simple extensions of known theorems. We then show that in the complex case, the only additional freedom allowed is complex conjugation. Finally, we apply those results to characterize the Fourier transform between certain function spaces.

AB - In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a diffeomorphism of the underlying manifold (with a bit more freedom in families of continuous functions). Our results in the real case are mostly simple extensions of known theorems. We then show that in the complex case, the only additional freedom allowed is complex conjugation. Finally, we apply those results to characterize the Fourier transform between certain function spaces.

UR - http://www.scopus.com/inward/record.url?scp=84865337877&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-29849-3_3

DO - 10.1007/978-3-642-29849-3_3

M3 - פרק

AN - SCOPUS:84865337877

SN - 9783642298486

T3 - Lecture Notes in Mathematics

SP - 35

EP - 59

BT - Geometric Aspects of Functional Analysis

PB - Springer Verlag

ER -