Displaying similar documents to “Necessary and sufficient conditions for a system of eigenfunctions and associated functions of a Sturm-Liouville operator with discontinuous coefficients to possess the basis property.”

Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

Annales de l'institut Fourier

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We establish a Carleman type inequality for the subelliptic operator ℒ = Δ z + | x | 2 ∂ t 2 in ℝ n + 1 , n ≥ 2 , where z ∈ ℝ n , t ∈ ℝ . As a consequence, we show that - ℒ + V has the strong unique continuation property at points of the degeneracy manifold { ( 0 , t ) ∈ ℝ n + 1 | t ∈ ℝ } if the potential V is locally in certain L p spaces.

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) ≤ λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ₂ ( 2 ) ) ≥ λ ( V ) for any two-dimensional real symmetric space V.

Integrable systems in the plane with center type linear part

Javier Chavarriga (1994)

Applicationes Mathematicae

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We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.