Values of modular functions at real quadratics and conjectures of Kaneko
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DOI: 10.1007/s00208-020-01979-6
Abstract: In 2008, Kaneko made several interesting observations about the values of the modular j invariant at real quadratic irrationalities. The values of modular functions at real quadratics are defined in terms of their cycle integrals… read more here.
Keywords: values modular; modular functions; real quadratics; conjectures kaneko ... See more keywords
A Schwarz Lemma for Harmonic Functions in the Real Unit Ball
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DOI: 10.1007/s10473-019-0512-z
Abstract: We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen’s Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping. read more here.
Keywords: harmonic functions; schwarz lemma; unit ball; functions real ... See more keywords
Singularities of slice regular functions over real alternative ⁎-algebras
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DOI: 10.1016/j.aim.2016.10.009
Abstract: Abstract The main goal of this work is classifying the singularities of slice regular functions over a real alternative ⁎-algebra A. This function theory has been introduced in 2011 as a higher-dimensional generalization of the… read more here.
Keywords: slice regular; slice; regular functions; real alternative ... See more keywords
Characterization of Fourier transform of $H$-valued functions on the real line
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DOI: 10.1216/rmj.2021.51.43
Abstract: A characterization is obtained for the Fourier transform of functions belonging to ℒ2(ℝ,H), where H denotes a Hilbert C∗-module. But in the case of functions belonging to L1(ℝ,H) a similar result is proved when H… read more here.
Keywords: characterization; valued functions; transform valued; fourier transform ... See more keywords