scholarly journals Complete Bernstein functions and subordinators with nested ranges. A note on a paper by P. Marchal

2016 ◽  
Vol 21 (0) ◽  
Author(s):  
Chang-Song Deng ◽  
René L. Schilling
Keyword(s):  
Bernstein Functions ◽  
Complete Bernstein Functions

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.

scholarly journals Perturbation determinants on Banach spaces and operator differentiability for Hirsch functional calculus

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1105-1115
Author(s):  
A.R. Mirotin
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Functional Calculus ◽  
Logarithmic Derivative ◽  
Bernstein Functions ◽  
Fréchet Differentiability ◽  
Frechet Differentiability ◽  
Complete Bernstein Functions ◽  
Perturbation Determinant

We consider a perturbation determinant for pairs of nonpositive (in a sense of Komatsu) operators on Banach space with nuclear difference and prove the formula for the logarithmic derivative of this determinant. To this end the Frechet differentiability of operator monotonic (negative complete Bernstein) functions of negative and nonpositive operators on Banach spaces is investigated. The results may be regarded as a contribution to the Hirsch functional calculus.

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