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OPERATORVALUED NONSTATIONARY SZEG0 LIMIT THEOREMS
"... ABSTRACT. The nonstationary extensions of two wellknown limit theorems of Szeg5 are proved for generaJized determinants. The main tool is e [ determinantal formula for positive block operators with HilbertSchmidt offdie[gonal entries in terms of Schur parameters. Applice[tions to prediction the ..."
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ABSTRACT. The nonstationary extensions of two wellknown limit theorems of Szeg5 are proved for generaJized determinants. The main tool is e [ determinantal formula for positive block operators with HilbertSchmidt offdie[gonal entries in terms of Schur parameters. Applice[tions to predic
Bernstein measures on convex polytopes
, 805
"... We define the notion of Bernstein measures and Bernstein approximations over general convex polytopes. This generalizes wellknown Bernstein polynomials which are used to prove the Weierstrass approximation theorem on one dimensional intervals. We discuss some properties of Bernstein measures and ap ..."
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We define the notion of Bernstein measures and Bernstein approximations over general convex polytopes. This generalizes wellknown Bernstein polynomials which are used to prove the Weierstrass approximation theorem on one dimensional intervals. We discuss some properties of Bernstein measures
Coefficients of orthogonal polynomials on the unit circle and higher order Szeg5 theorems
, 2005
"... Abstract. Let µ be a nontrivial probability measure on the unit circle ∂D, w the density of its absolutely continuous part, αn its Verblunsky coefficients, and Φn its monic orthogonal polynomials. In this paper we compute the coefficients of Φn in terms of the αn. If the function log w is in L 1 (d ..."
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Cited by 8 (0 self)
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Abstract. Let µ be a nontrivial probability measure on the unit circle ∂D, w the density of its absolutely continuous part, αn its Verblunsky coefficients, and Φn its monic orthogonal polynomials. In this paper we compute the coefficients of Φn in terms of the αn. If the function log w is in L 1
Jonathan Bernstein
"... The need exists for highsensitivity, lownoise vibration sensors for various applications such as geophysical data collection, vehicle tracking, intrusion detection, and underwater pressure gradient detection. In general, these sensors differ from classical accelerometers in that they require no dc ..."
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The need exists for highsensitivity, lownoise vibration sensors for various applications such as geophysical data collection, vehicle tracking, intrusion detection, and underwater pressure gradient detection. In general, these sensors differ from classical accelerometers in that they require no dc response, but must have a very low noise floor over a required bandwidth. Theory indicates a capacitive micromachined silicon vibration sensor can have a noise floor on the order of 100 ng/√Hz over a 1kHz bandwidth while reducing size and weight 10fold compared to existing magnetic geophones. With early prototypes, we have demonstrated Brownianlimited noise floor at 1.0 µg/ √Hz, orders of magnitude more sensitive than commercially available surface micromachined devices.
SZEG}O COORDINATES, QUADRATURE DOMAINS, AND DOUBLE QUADRATURE DOMAINS
"... Abstract. We dene Szeg}o coordinates on a nitely connected smoothly bounded planar domain which eect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature domain with respect to boundary arc length. When these S ..."
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Cited by 2 (2 self)
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Abstract. We dene Szeg}o coordinates on a nitely connected smoothly bounded planar domain which eect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature domain with respect to boundary arc length. When
Bernstein equiconvergence and Fejér type theorems for general rational Fourier series
, 1999
"... Let w(`) be a positive weight function on the interval [\Gammaß; ß) and associate the positive definite inner product on the unit circle of the complex plane by hf; gi w = 1 2ß R ß \Gammaß f(e i` )g(e i` )w(`)d`. For a sequence of points fff k g 1 k=1 included in a compact subset of the ..."
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Dini condition and that it is bounded away from zero. This generalizes a theorem given by Szeg...
SZEG O POLYNOMIALS: A VIEW FROM THE RIEMANNHILBERT WINDOW
"... Functions Tech04. We survey some recent results on canonical representation and asymptotic behavior of polynomials orthogonal on the unit circle with respect to an analytic weight. These results are obtained using the steepest descent method based on the RiemannHilbert characterization of these po ..."
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Functions Tech04. We survey some recent results on canonical representation and asymptotic behavior of polynomials orthogonal on the unit circle with respect to an analytic weight. These results are obtained using the steepest descent method based on the RiemannHilbert characterization of these polynomials.
CERTIFICATE This is to certify that the thesis entitled ·ON SZEG(YS TYPE
, 2003
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