Abstract
We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the direct computations in the shifts of singularities and the higher dimensional cases.
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Chihara, H.: Bounded Berezin–Toeplitz operators on the Segal–Bargmann space. Integral Equ. Oper. Theory 63, 321–335 (2009)
Chihara, H.: Bargmann-type transforms and modified harmonic oscillators (submitted). arXiv:1702.06646
Folland, G.B.: Harmonic Analysis in Phase Space. Princeton University Press, Princeton (1989)
Kagawa, T.: The Hermite function expansions of the Heaviside function. J. Pseudo Differ. Oper. Appl. 6, 21–32 (2015)
Simon, B.: Distributions and their Hermite expansions. J. Math. Phys. 12, 140–148 (1971)
Sjöstrand, J.: Function spaces associated to global I-Lagrangian manifolds. In: Morimoto, M., Kawai, T. (eds.) Structure of Solutions to Differential Equations (Katata/Kyoto 1995), pp. 369–423. World Scientific Publishing, River Edge (NJ) (1996)
Wong, M.W.: Weyl Transforms. Springer, Berlin (1998)
Wong, M.W.: Partial Differential Equations: Topics in Fourier Analysis. CRC Press, Boca Raton (2014)
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Hiroyuki Chihara is supported by the JSPS Grant-in-Aid for Scientific Research #16K05221.
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Chihara, H., Furuya, T. & Koshikawa, T. Hermite expansions of some tempered distributions. J. Pseudo-Differ. Oper. Appl. 9, 105–124 (2018). https://doi.org/10.1007/s11868-017-0211-2
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DOI: https://doi.org/10.1007/s11868-017-0211-2