Entropy of Hermite polynomials with application to the harmonic oscillator.

Van Assche, Walter

Displaying similar documents to “Entropy of Hermite polynomials with application to the harmonic oscillator.”

Free and classical entropy over the circle.

Blower, Gordon (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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The degree of the splitting field of a random polynomial over a finite field.

Dixon, John D., Panario, Daniel (2004)

The Electronic Journal of Combinatorics [electronic only]

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Optimal discrete entropy.

Shastri, Aditya, Govil, Rekha (2001)

Applied Mathematics E-Notes [electronic only]

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Counting irreducible polynomials over finite fields

Qichun Wang, Haibin Kan (2010)

Czechoslovak Mathematical Journal

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In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: $π (x) = \frac{q}{q - 1} \frac{x}{{log}_{q} x} + \frac{q}{{(q - 1)}^{2}} \frac{x}{{log}_{q}^{2} x} + O (\frac{x}{{log}_{q}^{3} x}), x = q^{n} \to \infty$ where $π (x)$ denotes the number of monic irreducible polynomials in $F_{q} [t]$ with norm $\leq x$ .

Replicant compression coding in Besov spaces

Gérard Kerkyacharian, Dominique Picard (2003)

ESAIM: Probability and Statistics

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We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space $B_{π, q}^{s}$ on a regular domain of $ℝ^{d} .$ The result is: if $s - d {(1 / π - 1 / p)}_{+}$ $> 0,$ then the Kolmogorov metric entropy satisfies $H (ϵ) \sim ϵ^{- d / s}$ . This proof takes advantage of the representation of such spaces on wavelet type bases and extends the result to more general spaces. The lower bound is a consequence of very simple probabilistic exponential inequalities. To prove the upper bound, we provide...

A short proof of a series evaluation in terms of harmonic numbers.

Panholzer, Alois, Prodinger, Helmut (2009)

Integers

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An Omega theorem on differences of two squares.

Kühleitner, M. (1992)

Acta Mathematica Universitatis Comenianae. New Series

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Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations

Shy-Der Lin, Shuoh-Jung Liu, Han-Chun Lu, Hari Mohan Srivastava (2013)

Czechoslovak Mathematical Journal

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The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as...

Logarithmic coefficients of univalent functions.

Girela, Daniel (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

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Some subclasses of close-to-convex functions

Adam Lecko (1993)

Annales Polonici Mathematici

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For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes $C_{β} (α)$ defined as follows: a function f regular in U = z: |z| < 1 of the form $f (z) = z + \sum_{n = 1}^{\infty} a_{n} z^{n}$ , z ∈ U, belongs to the class $C_{β} (α)$ if $R e e^{i β} (1 - α ² z ²) f^{'} (z) < 0$ for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in $C_{β} (α)$ are examined.