scholarly journals Bernstein inequality and holonomic modules

2017 ◽  
Vol 308 ◽  
pp. 941-963 ◽  
Author(s):  
Ivan Losev
Keyword(s):  
Bernstein Inequality ◽  
Holonomic Modules

scholarly journals Holonomic modules for rings of invariant differential operators

2021 ◽  
pp. 1-18
Author(s):  
Vyacheslav Futorny ◽  
João Schwarz
Keyword(s):  
Differential Operators ◽  
Main Tool ◽  
Bernstein Inequality ◽  
Invariant Differential Operators ◽  
Weyl Algebras ◽  
Invariant Differential ◽  
Quotient Varieties ◽  
Generalized Weyl Algebras ◽  
A Finite Group ◽  
Holonomic Modules

We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals [Formula: see text].

scholarly journals Cohen–Macaulay Modules and Holonomic Modules Over Filtered Rings

2009 ◽  
Vol 37 (2) ◽  
pp. 406-430
Author(s):  
Hiroki Miyahara ◽  
Kenji Nishida
Keyword(s):  
Holonomic Modules

scholarly journals On the Bernstein Inequality for Rational Functions with a Prescribed Zero

1998 ◽  
Vol 95 (3) ◽  
pp. 476-496 ◽  
Author(s):  
Roy Jones ◽  
Xin Li ◽  
R.N. Mohapatra ◽  
R.S. Rodriguez
Keyword(s):  
Rational Functions ◽  
Bernstein Inequality

scholarly journals Bernstein-type inequality for a class of dependent random matrices

2016 ◽  
Vol 05 (02) ◽  
pp. 1650006 ◽  
Author(s):  
Marwa Banna ◽  
Florence Merlevède ◽  
Pierre Youssef
Keyword(s):  
Random Matrices ◽  
Type Inequality ◽  
Bernstein Inequality ◽  
Mathematical Statistics ◽  
Strong Mixing ◽  
Mixing Conditions ◽  
Bernstein Type ◽  
Bernstein Type Inequality ◽  
The Matrix ◽  
The Laplace Transform

In this paper, we obtain a Bernstein-type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix setting of the Bernstein-type inequality obtained by Merlevède et al. [Bernstein inequality and moderate deviations under strong mixing conditions, in High Dimensional Probability V: The Luminy Volume, Institute of Mathematical Statistics Collection, Vol. 5 (Institute of Mathematical Statistics, Beachwood, OH, 2009), pp. 273–292.] in the context of real-valued bounded random variables that are geometrically absolutely regular. The proofs rely on decoupling the Laplace transform of a sum on a Cantor-like set of random matrices.

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