Triangular Dirichlet Kernels and Growth of L
p
Lebesgue Constants |
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Authors: | Marshall Ash |
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Institution: | 1. DePaul University, Chicago, IL, USA
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Abstract: | Let P be a polygon in ℤ2 and consider the mapping of an
L1(\mathbbT2)L^{1}(\mathbb{T}^{2})
function into the partial sum of its Fourier series determined by the dilate of P by the integer N. If the image space is endowed with the L
p
norm, 1<p<∞, then the operator norm will be given by the L
p
norm of ∑(m,n)∈NP
e
2π
i(mx+ny). The size of this operator norm is shown to be O(N
2(1−1/p)) when the polygon is a triangle. The estimate is independent of the shape of the triangle. For a k sided polygon the corresponding estimate is O(kN
2(1−1/p)). |
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Keywords: | |
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