Characterization of compact subsets of algebraic varieties in terms of Bernstein type inequalities

Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.

Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves

M. Baran, W. Pleśniak (1997)

Studia Mathematica

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We show that in the class of compact, piecewise $C^{1}$ curves K in $ℝ^{n}$ , the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.

A partial differential operator which is surjective on Gevrey classes $Γ^{d} (ℝ ³)$ with 1 ≤ d < 2 and d ≥ 6 but not for 2 ≤ d < 6

Rüdiger Braun (1993)

Studia Mathematica

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It is shown that the partial differential operator $P (D) = \partial ⁴ / \partial x ⁴ - \partial ² / \partial y ² + i \partial / \partial z : Γ^{d} (ℝ ³) \to Γ^{d} (ℝ ³)$ is surjective if 1 ≤ d < 2 or d ≥ 6 and not surjective for 2 ≤ d < 6.

Lattice points in a sphere

M. Bleicher, M. Knopp (1965)

Acta Arithmetica

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Mean square of the remainder term in the Dirichlet divisor problem

Yuk-Kam Lau, Kai-Man Tsang (1995)

Journal de théorie des nombres de Bordeaux

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