Abstract
Babuška introduced the concept of periodic Hilbert spaces for studying universally optimal quadrature formulas. Prager continued these investigations and discovered the relationship between optimal approximation of linear functionals on periodic Hilbert spaces and minimum norm interpolation ( optimal periodic interpolation ). In the case of a uniform mesh methods of periodic interpolation by translation are applicable and relations to periodic spline interpolation and approximation have been studied. It is the objective of this paper to introduce the concept of harmonic Hilbert space in a multivariate setting as an extension of periodic Hilbert space and to study approximation via Fourier partial integrals and exponential-type interpolation in these spaces.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
