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Uncertainty relations for sets of self adjoint operators
Author(s) -
Held Stefan
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110413
Subject(s) - tensor product , invariant (physics) , dimension (graph theory) , pure mathematics , domain (mathematical analysis) , mathematics , wavelet , property (philosophy) , relation (database) , tensor (intrinsic definition) , uncertainty principle , algebra over a field , computer science , mathematical analysis , artificial intelligence , data mining , physics , philosophy , epistemology , mathematical physics , quantum mechanics , quantum
Uncertainty relations quantify the joint localisation in time respectively space domain and Fourier domain. For that reason they are an important tool in the design of wavelets. Uncertainty relations in higher dimension are most often realized as the tensor product of one dimensional uncertainty relations, whence these uncertainty relations are not invariant under rotations. The property of invariance with respect to rotation is however very desirable for image processing. We will give a new uncertainty relation for sets of self‐adjoint operators that yields the desired invariance in many examples. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)