Addendum: Multidimensional Analogue of Yu. V. Linnik’s Theorem on Decompositions of a Convolution of Gaussian and Poisson Laws

1967 ◽  
Vol 12 (3) ◽  
pp. 529-530
Author(s):  
I. V. Ostrovskii
Keyword(s):  
Multidimensional Analogue

Bounds for the Characteristic Functions of the System of Monomials in Random Variables and of Its Trigonometric Analogue

1997 ◽  
Vol 4 (6) ◽  
pp. 579-584
Author(s):  
T. Shervashidze
Keyword(s):  
Random Vector ◽  
Continuous Distribution ◽  
Random Variables ◽  
Upper Bounds ◽  
Characteristic Functions ◽  
Absolutely Continuous ◽  
Multidimensional Analogue ◽  
Trigonometric Integral

Abstract Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in and of the system (cos j 1πξ 1 . . . cos j s πξ s , 0 ≤ j 1, . . . , j s ≤ k, j 1 + . . . + j s ≥ 1), where (ξ 1, . . . , ξ s ) is uniformly distributed in [0; 1] s .

scholarly journals Characterizations of Herglotz–Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables

2021 ◽  
Vol 15 (7) ◽  
Author(s):  
Mitja Nedic
Keyword(s):  
Holomorphic Functions ◽  
Negative Real Part ◽  
Nevanlinna Function ◽  
Multidimensional Analogue ◽  
Several Variables ◽  
Nevanlinna Functions ◽  
Unit Polydisk ◽  
Definition Of ◽  
Poisson Type

AbstractIn this paper, we give several characterizations of Herglotz–Nevanlinna functions in terms of a specific type of positive semi-definite functions called Poisson-type functions. This allows us to propose a multidimensional analogue of the classical Nevanlinna kernel and a definition of generalized Nevanlinna functions in several variables. Furthermore, a characterization of the symmetric extension of a Herglotz–Nevanlinna function is also given. The subclass of Loewner functions is discussed as well, along with an interpretation of the main result in terms of holomorphic functions on the unit polydisk with non-negative real part.

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