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12 results on '"S B Damelin"'

1. On Surface Completion and Image Inpainting by Biharmonic Functions: Numerical Aspects

Author

S. B. Damelin and N. S. Hoang

Subjects
Mathematics, QA1-939
Abstract

Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal derivatives of the functions on the boundary. Finite difference schemes for solving these harmonic functions are discussed in detail.

Published
2018
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2. Local Paley–Wiener theorems for functions analytic on unit spheres

Author

S B Damelin and Anthony J. Devaney

Subjects
Unit sphere, Pure mathematics, Euclidean space, Applied Mathematics, Function (mathematics), Mathematical proof, Computer Science Applications, Theoretical Computer Science, law.invention, Algebra, symbols.namesake, Invertible matrix, Fourier transform, law, Bounded function, Signal Processing, symbols, Unit (ring theory), Mathematical Physics, Mathematics
Abstract

The purpose of this paper is to provide new and simplified statements of local Paley?Wiener theorems on the (n ? 1)-dimensional unit sphere realized as a subset of n = 2, 3 Euclidean space. More precisely, given a function , whose restriction to an n ? 1 sphere is analytic, we establish necessary and sufficient conditions determining whether f is the Fourier transform of a compactly supported, bounded function . The essence of this investigation is that, because of the local nature of the problem, the mapping f ? F is not in general invertible and so the problem cannot be studied via a Fourier integral. Our proofs are new.

Published
2007

4. [Untitled]

Author

B. Bajnok, S. B. Damelin, J. Li, and G. L. Mullen

Subjects
Surface (mathematics), Numerical Analysis, Scattering, Mathematical analysis, Geometry, Harmonic polynomial, Potential theory, Computer Science Applications, Theoretical Computer Science, Computational Mathematics, Finite field, Computational Theory and Mathematics, Harmonic function, Quadratic form, Spherical design, Software, Mathematics
Abstract

We use solutions to quadratic forms in d + 1 variables over finiter fields to scatter points the surface of the unit shpere S ,d 1. Applications are given for spherical t designs and generalized s energies.

Published
2002

5. Necessary conditions for weighted mean convergence of Lagrange interpolation for exponential weights

Author

S. B. Damelin, HS Jung, and Kiok Kwon

Subjects
Weight function, Applied Mathematics, Mathematical analysis, Lagrange polynomial, Lagrange interpolation, Orthogonal polynomial, Function (mathematics), Weighted approximation, Weighted geometric mean, Exponential function, Computational Mathematics, symbols.namesake, Freud weight, Convergence (routing), symbols, Erdős weight, Exponential decay, Real line, Pollaczek weight, Mathematics
Abstract

Given a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (−1,1).

Published
2001

6. Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights II

Author

S. B. Damelin and D. S. Lubinsky

Subjects
General Mathematics, 010102 general mathematics, 0103 physical sciences, 010307 mathematical physics, 0101 mathematics, 01 natural sciences
Abstract

We complete our investigations of mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn(W2, x) for Erdős weights W2 = e-2Q. The archetypal example is Wk,α = exp(—Qk,α), whereα > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 < p < 4 and α ∊ ℝ Let Ln[f] denote the Lagrange interpolation polynomial to ƒ at the zeros of pn(W2, x) = pn(e-2Q, x). Then forto hold for every continuous function ƒ:ℝ. —> ℝ satisfyingit is necessary and sufficient that α > 1/p. This is, essentially, an extension of the Erdös-Turan theorem on L2 convergence. In an earlier paper, we analyzed convergence for all p > 1, showing the necessity and sufficiency of using the weighting factor 1 + Q for all p > 4. Our proofs of convergence are based on converse quadrature sum estimates, that are established using methods of H. König.

Published
1996

8. The Cardinality of Sets of k -Independent Vectors over Finite Fields.

Author

S. B. Damelin, G. Michalski, and Gary L. Mullen

Abstract

Abstract.  A set of vectors isk-independent if all its subsets with no more thankelements are linearly independent. We obtain a result concerning the maximal possible cardinality Indq(n,k) of ak-independent set of vectors in then-dimensional vector spaceFqnover the finite fieldFqof orderq. Namely, we give a necessary and sufficient condition for Indq(n,k) =n+ 1. We conclude with some pertinent remarks re applications of our results to codes, graphs and hypercubes. [ABSTRACT FROM AUTHOR]

Published
2007
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9. The Number of Linearly Independent Binary Vectors with Applications to the Construction of Hypercubes and Orthogonal Arrays, Pseudo ( t, m, s)-Nets and Linear Codes.

Author

S. B. Damelin, G. Michalski, G. L. Mullen, and D. Stone

Subjects
BIVECTORS, HYPERCUBES, ORTHOGONAL arrays, LINEAR programming
Abstract

We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1?=?k?=? n. Applications are given to the design of hypercubes and orthogonal arrays, pseudo ( t, m, s)-nets and linear codes. [ABSTRACT FROM AUTHOR]

Published
2004

11. Weighted Polynomials on Discrete Sets.

Author

S. B. Damelin

Subjects
POLYNOMIALS, DISCRETE groups, INFINITE groups, INFINITE integrals
Abstract

Abstract. For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous Lp (0 < p  ∞) norm of a weighted polynomial, Pnwn, deg Pn  n, n  1 is in an nth root sense, controlled by its corresponding discrete Hölder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish ${\rm Nikol'ski{\breve \i}}$ inequalities and theorems dealing with zero distribution, zero location and sup and Lp infinite-finite range inequalities. [ABSTRACT FROM AUTHOR]

Published
2003

12. The support of the equilibrium measure in the presence of a monomial external field on $[-1,1]$.

Author

S. B. Damelin and A. B. J. Kuijlaars

Subjects
*EQUILIBRIUM, *RINGS of integers
Abstract

The support of the equilibrium measure associated with an external field of the form $Q(x) = - cx^{2m+1}$, $x \in [-1,1]$, with $c > 0$ and $m$ a positive integer is investigated. It is shown that the support consists of at most two intervals. This resolves a question of Deift, Kriecherbauer and McLaughlin. [ABSTRACT FROM AUTHOR]

Published
1999
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