Certain algebras generated by the multidimensional analogue of the bitsadze operator

1988 ◽  
Vol 28 (5) ◽  
pp. 847-849
Author(s):  
V. B. Cherdak



2012 ◽  
Vol 76 (4) ◽  
pp. 681-687 ◽  
Author(s):  
Vladimir A Klyachin




1995 ◽  
Vol 186 (2) ◽  
pp. 257-269 ◽  
Author(s):  
V A Okulov




1997 ◽  
Vol 4 (6) ◽  
pp. 579-584
Author(s):  
T. Shervashidze

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 .



2021 ◽  
Vol 15 (7) ◽  
Author(s):  
Mitja Nedic

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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