Sharp interpolation inequalities for discrete operators and applications

2014/07/02 by Alexei Ilyin, Ilyin, Alexei, Ари Лаптев +3
Mathematics · Engineering · Computer Science · #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1407.0675

Abstract

We consider interpolation inequalities for imbeddings of the l²-sequence spaces over d-dimensional lattices into the l^∞₀ spaces written as interpolation inequality between the l²-norm of a sequence and its difference. A general method is developed for finding sharp constants, extremal elements and correction terms in this type of inequalities. Applications to Carlson's inequalities and spectral theory of discrete operators are given.

Related

• Several inequalities concerning interpolation in classical Fourier analysis
• L²-interpolation with error and size of spectra
• Limiting interpolation spaces via extrapolation
• Bennett-Carl inequalities for symmetric Banach sequence spaces and unitary ideals
• Interpolating sequences for H^∞(B_H)