Alex Grossmann, from Nested Hilbert Spaces to Partial Inner Product Spaces and Wavelets

Antoine, Jean-Pierre
(2023) Theoretical Physics, Wavelets, Analysis, Genomics. An Interdisciplinary Tribute to Alex Grossmann — ISBN: [978-3-030-458476-1 978-3-030-45847-8 (eBook)], p. 63-79, published

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  • Antoine, Jean-Pierreorcid-logoUCLouvain
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Abstract
This chapter is devoted to the long collaboration between Alex Grossmann and I, the focal point being the notion of partial Inner Spaces, introduced around 1970. Next I will review the basic facts of the theory. Then I will explore all the consequences and applications of that notion, to operator theory, spectral analysis of self-adjoint operators, metric operators that generate lattices of Hilbert spaces, signal processing, etc. As a matter of fact, new developments are still arising today. In addition, we'll describe the interaction with Alex that lead to 2D continuous wavelets.
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Antoine, J.-P. (2023). Alex Grossmann, from Nested Hilbert Spaces to Partial Inner Product Spaces and Wavelets. In P. Flandrin, S. Jaffard, T. Paul and B. Torrésani (eds) (ed.), Theoretical Physics, Wavelets, Analysis, Genomics. An Interdisciplinary Tribute to Alex Grossmann (p. p. 63-79). Birkhäuser. https://doi.org/10.1007/978-3-030-45847-8