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Restricted interpolation by meromorphic inner functions

100%

Poltoratski A., Rupam R.

Concrete Operators

2016

tom 3

nr 1

102-111

Meromorphic Inner Functions (MIFs) on the upper half plane play an important role in applications to spectral problems for differential operators. In this paper, we survey some recent results concerning function theoretic properties of MIFs and show their connections with spectral problems for the Schrödinger operator.

A geometric estimate for a periodic Schrödinger operator

88%

Friedrich T.

Colloquium Mathematicum

2000

tom 83

nr 2

209-216

We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator $-4{d^2}/{ds^2} + κ^2(s)$ with potential given by the curvature of a closed curve.

Some remarks on Bochner-Riesz means

75%

Thangavelu S.

Colloquium Mathematicum

2000

tom 83

nr 2

217-230

We study $L^p$ norm convergence of Bochner-Riesz means $S_R^δ f$ associated with certain non-negative differential operators. When the kernel $S_R^m(x,y)$ satisfies a weak estimate for large values of m we prove $L^p$ norm convergence of $S_R^δ f$ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Concrete Operators

1 Friedrich T.

1 Poltoratski A.

1 Rupam R.

1 Thangavelu S.

1 2016

2 2000

Wyniki wyszukiwania

Restricted interpolation by meromorphic inner functions

A geometric estimate for a periodic Schrödinger operator

Some remarks on Bochner-Riesz means