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 at In particular, we show that the differential Galois group of this eigenvalue problem is reductive at generic eigenvalues. In the preceding paper [AT] compactness propertiesCn andCPn for locally compact groups were introduced. Simple modules over the multiparameter quantum function algebra at roots of 1 We also prove that iff(X,Y) is a polynomial overC with one place at infinity, then for every λ∈C,f-λ also has one place at infinity. The Bloch-Okounkov correlation functions at higher levels A new deformation parameter arises: one can deform the formal normal forms of connections at irregular points. The proof uses some new results due to Koras and Russell on contractible surfaces with at most quotient singularities and also several results about reductive group actions on affine varieties. We consider free affine actions of unipotent complex algebraic groups on Cn and prove that such actions admit an analytic geometric quotient if their degree is at most 2. One outcome is a simple proof that for $g_{m \alpha , n \beta}$ to span $L^2,$ the lattice $(m \alpha , n \beta )$ must have at least unit density. The theorem is then used to characterize a class of entire functions that can be reconstructed from their sample values at the points tn = an + b if n = 0, 1, 2, ... In addition, if the scaling functions have at least asymptotic linear phase, then we prove that they converge to the "sinc" function and their corresponding orthonormal wavelets converge to the "difference" of two sinc functions. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. In this article we consider the question when one can generate a Weyl- Heisenberg frame for l2(?) with shift parameters N, M-1 (integer N, M) by sampling a Weyl-Heisenberg frame for L2(?) with the same shift parameters at the integers. It is shown that this is possible when the window g ε L2(?) generating the Weyl-Heisenberg frame satisfies an appropriate regularity condition at the integers. Here we consider more generally the classical Banach spacesEp(1 ≤ p ≤ ∞) consisting of all entire functions of exponential type at most π that belong to Lp (-∞, ∞) on the real axis. We compute their H?lder regularity and oscillation at every point and we deduce their spectrum of oscillating singularities. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. In a much cited article, Yau [5] proved that when the Ricci curvature is bounded uniformly below, then the only bounded solution to the heat equation ?tμ=Δμ on [0, ∞) × M which vanishes at t=0 is the one which vanishes evarywhere. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].

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2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社