publication . Preprint . 2013

A connection between the Uncertainty Principles on the real line and on the circle

Andersen, Nils Byrial;
Open Access English
  • Published: 18 Jul 2013
Abstract
The purpose of this short note is to exhibit a new connection between the Heisenberg Uncertainty Principle on the line and the Breitenberger Uncertainty Principle on the circle, by considering the commutator of the multiplication and difference operators on Bernstein functions
Subjects
free text keywords: Mathematics - Functional Analysis
Download from

[1] E. Breitenberger, Uncertainty measures and uncertainty relations for angle observables, Found. Phys. 15 (1983), 353-364.

[2] W. Erb, Uncertainty principles on Riemannian manifolds, Dissertation, Logos Verlag, Berlin (2011).

[3] G.B. Folland, A. Sitaram, The uncertainty principle: a mathematical survey, J. Fourier Anal. Appl. 3 (1997), 207-233. [OpenAIRE]

[4] T.N.T. Goodman, S.S. Goh, Uncertainty principles and optimality on circles and spheres, Advances in constructive approximation: Vanderbilt 2003, 207218, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2004.

[5] S.S. Goh, T.N.T. Goodman, Uncertainty principles and asymptotic behavior, Appl. Comput. Harmon. Anal. 16 (2004), 19-43.

[6] S.S. Goh, C.A. Micchelli, Uncertainty principles in Hilbert spaces, J. Fourier Anal. Appl. 8 (2002), 335-373.

[7] W. Heisenberg, U¨ ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. f. Physik. 43 (1927), 172-198. [OpenAIRE]

[8] B.Ya. Levin, Lectures on entire functions, Translations of Mathematical Monographs, Vol. 150, Amer. Math. Soc., Providence, RI.

[9] J. Prestin, E. Quak, Optimal functions for a periodic uncertainty principle and multiresolution analysis, Proc. Edinburgh Math. Soc. (2) 42 (1999), 225-242. [OpenAIRE]

[10] J. Prestin, E. Quak, H. Rauhut, K. Selig, On the connection of uncertainty principles for functions on the circle and on the real line, J. Fourier Anal. Appl. 9 (2003), 387-409. [OpenAIRE]

[11] K. Selig, Uncertainty Principles revisited, Electron. Trans. Numer. Anal. 14 (2002), 165-177. Department of Mathematics, Aarhus University, Ny Munkegade 118, Building 1530, DK-8000 Aarhus C, Denmark E-mail address: byrial@imf.au.dk

Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue