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Search Results: 1 - 10 of 56 matches for " Vilmos Totik "
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Orthogonal Polynomials
Vilmos Totik
Surveys in Approximation Theory , 2005,
Abstract: In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
Orthogonal Polynomials
Vilmos Totik
Mathematics , 2005,
Abstract: In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
On a conjecture of Widom
Vilmos Totik,Peter Yuditskii
Mathematics , 2014,
Abstract: In 1969 Harold Widom published his seminal paper, which gave a complete description of orthogonal and Chebyshev polynomials on a system of smooth Jordan curves. When there were Jordan arcs present the theory of orthogonal polynomials turned out to be just the same, but for Chebyshev polynomials Widom's approach proved only an upper estimate, which he conjectured to be the correct asymptotic behavior. In this note we make some clarifications which will show that the situation is more complicated.
Christoffel functions with power type weights
Tivadar Danka,Vilmos Totik
Mathematics , 2015,
Abstract: Precise asymptotics for Christoffel functions are established for power type weights on unions of Jordan curves and arcs. The asymptotics involve the equilibrium measure of the support of the measure. The result at the endpoints of arc components is obtained from the corresponding asymptotics for internal points with respect to a different power weight. On curve components the asymptotic formula is proved via a sharp form of Hilbert's lemniscate theorem while taking polynomial inverse images. The situation is completely different on the arc components, where the local asymptotics is obtained via a discretization of the equilibrium measure with respect to the zeros of an associated Bessel function. The proofs are potential theoretical, and fast decreasing polynomials play an essential role in them.
Limits of Zeros of Orthogonal Polynomials on the Circle
Barry Simon,Vilmos Totik
Mathematics , 2004,
Abstract: We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a question of Tur\'an): namely, for $n
Asymptotically sharp Markov and Schur inequalities on general sets
Sergei Kalmykov,Bela Nagy,Vilmos Totik
Mathematics , 2014, DOI: 10.1007/s11785-014-0405-z
Abstract: Markov's inequality for algebraic polynomials on $\left[-1,1\right]$ goes back to more than a century and it is widely used in approximation theory. Its asymptotically sharp form for unions of finitely many intervals has been found only in 2001 by the third author. In this paper we extend this asymptotic form to arbitrary compact subsets of the real line satisfying an interval condition. With the same method a sharp local version of Schur's inequality is given for such sets.
On the stabilization of the Korteweg–de Vries equation
Vilmos Komornik
Boletim da Sociedade Paranaense de Matemática , 2010,
Abstract: We consider the Korteweg–de Vries equation on a bounded intervalwith periodic boundary conditions. We prove that a natural mass conserving global feedback exponentially stabilizes the system in all Sobolev norms and we obtain explicit decay rates. The proofs are based on the family of conservation laws for the Korteweg–de Vries equation.
Uniformly bounded Riesz bases and equiconvergence theorems
Vilmos Komornik
Boletim da Sociedade Paranaense de Matemática , 2007,
Abstract: We review some classical results on the convergence of classical trigonometric and polynomial Fourier series. Then we present a not well-known short proof of the local uniform boundedness of many classical orthonormal systems. Finally, we formulate a strong generalization of Haar's classical equiconvergence theorem.
On the exactness of the Levy-transformation
Vilmos Prokaj
Mathematics , 2014,
Abstract: In a recent paper we gave a sufficient condition for the strong mixing property of the Levy-transformation. In this note we show that it actually implies a much stronger property, namely exactness.
Explicit multidimensional Ingham--Beurling type estimates
Vilmos Komornik
Mathematics , 2008,
Abstract: Recently a new proof was given for Beurling's Ingham type theorem on one-dimensional nonharmonic Fourier series, providing explicit constants. We improve this result by applying a short elementary method instead of the previous complex analytical approach. Our proof equally works in the multidimensional case.
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