scholarly journals Metric Spaces and Positive Definite Functions

1988 ◽  
pp. 100-114
Author(s):  
I. J. Schoenberg
Keyword(s):  
Metric Spaces ◽  
Positive Definite ◽  
Positive Definite Functions

Positive definite functions on spheres

1973 ◽  
Vol 73 (1) ◽  
pp. 145-156 ◽  
Author(s):  
N. H. Bingham
Keyword(s):  
Hilbert Space ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Distance ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Necessary Condition ◽  
Unit Hypersphere

Positive definite functions on metric spaces were considered by Schoenberg (26). We write σk for the unit hypersphere in (k + 1)-space; then σk is a metric space under geodesic distance. The functions which are positive definite (p.d.) on σk were characterized by Schoenberg (27), who also obtained a necessary condition for a function to be p.d. on the it sphere σ∞ in Hilbert space. We extend this result by showing that Schoenberg's necessary condition for a function to be p.d. on σ∞ is also sufficient.

scholarly journals A Gneiting-Like Method for Constructing Positive Definite Functions on Metric Spaces

2020 ◽  
Author(s):  
Victor S. Barbosa ◽  
◽  
Valdir A. Menegatto ◽  
◽  
◽  
...  
Keyword(s):  
Metric Spaces ◽  
Cartesian Product ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Established Method ◽  
Bernstein Functions ◽  
Necessary And Sufficient ◽  
Complete Bernstein Functions

This paper is concerned with the construction of positive definite functions on a cartesian product of quasi-metric spaces using generalized Stieltjes and complete Bernstein functions. The results we prove are aligned with a well-established method of T. Gneiting to construct space-time positive definite functions and its many extensions. Necessary and sufficient conditions for the strict positive definiteness of the models are provided when the spaces are metric.

Strictly and Strongly Positive Definite Functions on Locally Compact Hypergroups

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
László Székelyhidi ◽  
Seyyed Mohammad Tabatabaie ◽  
Kedumetse Vati
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions ◽  
Locally Compact

scholarly journals Approximate solutions of equations defined by complex spherical multiplier operators

2005 ◽  
Vol 2005 (2) ◽  
pp. 93-115
Author(s):  
C. P. Oliveira
Keyword(s):  
Approximate Solutions ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Sobolev Type ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Solutions Of Equations ◽  
Multiplier Operators

This paper studies, in a partial but concise manner, approximate solutions of equations defined by complex spherical multiplier operators. The approximations are from native spaces embedded in Sobolev-type spaces and derived from the use of positive definite functions to perform spherical interpolation.

scholarly journals Extension of positive definite functions

2015 ◽  
Vol 422 (1) ◽  
pp. 712-740 ◽  
Author(s):  
Palle E.T. Jorgensen ◽  
Robert Niedzialomski
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions

Positive definite functions of infinitely many variables in a layer

1972 ◽  
Vol 24 (4) ◽  
pp. 351-372 ◽  
Author(s):  
Yu. M. Berezanskii ◽  
I. M. Gali
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions
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