Vol. 77, No. 1, 1978

Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Kernel dilation in reproducing kernel Hilbert space and its application to moment problems

Gary Doyle Faulkner and Ronald Wesley Shonkwiler

Vol. 77 (1978), No. 1, 103–115
Abstract

We give a reformulation of Nagy’s Principal Theorem in terms of a dilation of a family of operators in reproducing kernel Hilbert space. In this setting we are able to generalize Nagy’s result to obtain dilations K of reproducing kernels K derived from certain families of operators. We define the concept of positive type for kernels K whose values are unbounded operators on a Hilbert space. The construction of K is such that it possesses a property, which we call splitting, not enjoyed by K. We show that the splitting property constitutes the utility of dilation theory and use it to solve moment problems.

Mathematical Subject Classification 2000
Primary: 46E20
Secondary: 44A60, 47A20, 47B50
Milestones
Received: 21 April 1977
Revised: 18 December 1977
Published: 1 July 1978
Authors
Gary Doyle Faulkner
Ronald Wesley Shonkwiler