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Approximation By Rational Functions, Ronald A. Devore
Approximation By Rational Functions, Ronald A. Devore
Faculty Publications
Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If f' is in L log L on a finite interval, then f can be approximated in the uniform norm by rational functions of degree n to an error 0(1/n) on that interval.
Alfred Tarski And Undecidable Theories, George F. Mcnulty
Alfred Tarski And Undecidable Theories, George F. Mcnulty
Faculty Publications
No abstract provided.
On The Atomic Decomposition Of H^1 And Interpolation, Robert Sharpley
On The Atomic Decomposition Of H^1 And Interpolation, Robert Sharpley
Faculty Publications
© 1986 by American Mathematical Society
Nonexistence Of Stable Harmonic Maps To And From Certain Homogeneous Spaces And Submanifolds Of Euclidean-Space, Ralph Howard, S Walter Wei
Nonexistence Of Stable Harmonic Maps To And From Certain Homogeneous Spaces And Submanifolds Of Euclidean-Space, Ralph Howard, S Walter Wei
Faculty Publications
Call a compact Riemannian manifold M a strongly unstable manifold if it is not the range or domain of a nonconstant stable harmonic map and also the homotopy class of any map to or from M contains elements of arbitrarily small energy. If M is isometrically immersed in Euclidean space, then a condition on the second fundamental form of M is given which implies M is strongly unstable. As compact isotropy irreducible homogeneous spaces have "standard" immersions into Euclidean space this allows a complete list of the strongly unstable compact irreducible symmetric spaces to be made.
Multivariate Rational Approximation, Ronald A. Devore, Xiang Ming Yu
Multivariate Rational Approximation, Ronald A. Devore, Xiang Ming Yu
Faculty Publications
No abstract provided.
Sequences In Power Residue Classes, Duncan A. Buell, Richard H. Hudson
Sequences In Power Residue Classes, Duncan A. Buell, Richard H. Hudson
Faculty Publications
Using A. Weil’s estimates the authors have given bounds for the largest prime P0 such that all primes P > P0 have sequences of quadratic residues of length m. For m ≤ 8 the smallest prime having m consecutive quadratic residues is ≡ 3(mod 4) and P0 ≡ 1 (mod 4). The reason for this phenomenon is investigated in this paper and the theory developed is used to successfully uncover analogous phenomena for rth power residues, r ≥ 2, r even.