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- W2950149069 abstract "It does not seem to have been observed previously that the classical Bernstein polynomials $B_N(f)(x)$ are closely related to the Bergman-Szego kernels $Pi_N$ for the Fubini-Study metric on $CP^1$: $B_N(f)(x)$ is the Berezin symbol of the Toeplitz operator $Pi_N f(N^{-1} D_{theta})$. The relation suggests a generalization of Bernstein polynomials to any toric Kahler variety and Delzant polytope $P$. When $f$ is smooth, $B_N(f)(x)$ admits a complete asymptotic expansion. Integrating it over $P$ gives a complete asymptotic expansion for Dedekind-Riemann sums of smooth functions over lattice points in $N P$ related to Euler-MacLaurin sum formulae of Guillemin-Sternberg and others." @default.
- W2950149069 created "2019-06-27" @default.
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- W2950149069 date "2007-05-20" @default.
- W2950149069 modified "2023-09-27" @default.
- W2950149069 title "Bernstein polynomials, Bergman kernels and toric Kahler varieties" @default.
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