Abstract
By using amulti-dimensional analogue of the Mellin transform techniques we prove a multivariate multiplier theorem for general tensor product orthogonal expansions and a multivariate multiplier theorem for the Hankel transform.
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Acknowledgments
The author wishes to express his gratitude to Prof. Krzysztof Stempak, for numerous helpful remarks during the preparation of the paper, to Prof. Jacek Dziubański, for suggesting the improvement in the Appendix, and to Prof. Stefano Meda for an instructive conversation.
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Communicated by K. Gröchenig.
The research was supported by Polish Government funds for science—research project 2011/01/N/ST1/01785, NCN.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Wróbel, B. Multivariate spectral multipliers for tensor product orthogonal expansions. Monatsh Math 168, 125–149 (2012). https://doi.org/10.1007/s00605-011-0363-8
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DOI: https://doi.org/10.1007/s00605-011-0363-8