A Survey of Advances in Schwartz Linear Algebra: From Fourier Families to Generalized Dirac Products
Abstract
This paper surveys recent explorations into David Carf`ı’s Schwartz Linear Algebra, a framework unifying algebra, analysis, and quantum mechanics through Schwartz families and tempered distributions. We examine the Fourier kernel as a Schwartz basis, critique the Hilbert space foundation of quantum mechanics, and lay the groundwork for the generalized Dirac scalar product of transposable Schwartz families with tempered distributions. These developments address limitations in traditional quantum theory, offering a rigorous, distribution-based alternative.
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