Reproducing Kernel Hilbert Space vs. Frame Estimates

Mathematics

Myung-Sin Song¹  Palle E. T. Jorgensen² 

[1] Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Box 1653, Edwardsville, IL 62026, USA;Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA;

关键词: Hilbert space;    frames;    reproducing kernel;    Karhunen-Loève;   

DOI  :  10.3390/math3030615

来源: DOAJ

【 摘 要 】

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.

【 授权许可】

Unknown