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On some extremal problems in certain harmonic function spaces of several variables related to mixed norm spaces
Distance estimates harmonic function unit ball Bergman spaces
2012/5/9
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ...
Groups of formal diffeomorphisms in several complex variables and closed one-forms
Groups of formal diffeomorphisms several complex variables closed one-forms
2011/1/21
We study groups of formal diffeomorphisms in several complex variables. For abelian,metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential...
Separation of variables in one partial integrable case of Goryachev
Separation of variables partial integrable case of Goryachev
2010/12/28
We show that the equations of motion in one partial integrable case of Goryachev in the rigid body dynamics can be separated by the appropriate change of variables,the new variables x, y being hyperel...
The Curse of Dimensionality for Monotone and Convex Functions of Many Variables
Convex Functions Many Variables
2010/11/22
We study the integration and approximation problems for monotone and convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for al...
Limits of quotients of real analytic functions in two variables
quotients real analytic functions variables
2010/11/12
Necessary and sufficient conditions for the existence of limits of the form {equation*} \lim_{(x,y)\rightarrow (a,b)}\frac{f(x,y)}{g(x,y)} {equation*} are given, under the hipothesis that $f$ and $g$...
Operator monotone functions and Löwner functions of several variables
Operator monotone functions Lö wner functions of several variables
2010/12/9
We prove generalizations of L¨owner’s results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuti...
To any walk in a quiver, we associate a Laurent polynomial. When the walk is the string of a string module over a 2-Calabi-Yau tilted algebra, we prove that this Laurent polynomial coincides with the ...
Inequalities on the Variances of Convex Functions of Random Variables
Convex functions variance
2010/1/22
We develop inequalities relating to the variances of convex decreasing functions of random variables using information on the functions and the distribution functions of the random variables.
Inequalities of Maximum of Partial Sums and Weak Convergence for a Class Weak Dependent Random Variables
$\rho^{-}$-mixing $\rho^{*}$-mixing NA rosenthal type inequalities weak convergence
2007/12/12
In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for $\rho^{-}$-mixing random fields. As its applications we get the H\'{a}jeck--R\`{e}nyi inequality and weak con...
Stability of Functional Equations in Several Variables
stability functional equation Jordan homomorphism Lie homomorphism
2007/12/11
We prove a generalization of Hyers' theorem on the stability of approximately additive mapping and a generalization of Badora's theorem on an approximate ring homomorphism. We also obtain a more gener...
Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
Singular Points Eikonal Partial Differential Equations
2010/11/1
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equatio...