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Spherical Harmonics

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arxiv 1304.2585 v1 pith:BZAIGDFE submitted 2013-04-09 math.CA

F. Dai , Y. Xu This is my paper · ORCID
classification math.CA
keywords bookharmonicssphericalspringeranalysisapproximationattachedauthors
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This is Chapter 1 of the book {\it Approximation Theory and Harmonic Analysis on Spheres and Balls} by the authors. It provides a self-contained introduction to spherical harmonics. The book will be published as a title in {\it Springer Monographs in Mathematics} by Springer in 2013. The table of contents of the book is attached at the end of this file.

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  1. Exact distinguishability between real-valued and complex-valued Haar random quantum states

    quant-ph 2025-07 accept novelty 7.0 of 10

    The real Haar state twirl is diagonalized exactly, yielding the trace distance between real and complex Haar random states and new lower bounds on real-valued t-designs and imaginarity testing.

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