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Displaying 81 – 100 of 105

The Fekete-Szegő theorem with splitting conditions: Part I

Robert Rumely (2000)

Acta Arithmetica

The Fekete-Szegő theorem with splitting conditions: Part II

Robert Rumely (2002)

Acta Arithmetica

The form boundedness criterion for the relativistic Schrödinger operator

Vladimir Maz'ya, Igor Verbitsky (2004)

Annales de l’institut Fourier

We establish necessary and sufficient conditions on the real- or complex-valued potential $Q$ defined on $ℝ^{n}$ for the relativistic Schrödinger operator $\sqrt{- Δ} + Q$ to be bounded as an operator from the Sobolev space $W_{2}^{1 / 2} (ℝ^{n})$ to its dual $W_{2}^{- 1 / 2} (ℝ^{n})$ .

The homogeneous transfinite diameter of a compact subset of $ℂ^{N}$

Mieczysław Jędrzejowski (1991)

Annales Polonici Mathematici

Let K be a compact subset of $ℂ^{N}$ . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of $ℂ^{N}$ is computed.

The logarithmic capacity in $C^{n}$

S. Kołodziej (1988)

Annales Polonici Mathematici

The uniform norming of retractions on short intervals for certain function spaces.

Kalyabin, G.A. (1997)

Georgian Mathematical Journal

Trudinger's inequality for double phase functionals with variable exponents

Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura (2021)

Czechoslovak Mathematical Journal

Our aim in this paper is to establish Trudinger’s inequality on Musielak-Orlicz-Morrey spaces $L^{Φ, κ} (G)$ under conditions on $Φ$ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger’s inequality for double phase functionals $Φ (x, t) = t^{p (x)} + a (x) t^{q (x)}$ , where $p (\cdot)$ and $q (\cdot)$ satisfy log-Hölder conditions and $a (\cdot)$ is nonnegative, bounded and Hölder continuous.

Tusk type conditions and thinness for the parabolic operator of order ...

Miroslav Brzezina (1993)

Manuscripta mathematica

Voiculescu’s Entropy and Potential Theory

Thomas Bloom (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.