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Fractional Calculus and Applied Analysis, ISSN 1311-0454, 08/2015, Volume 18, Issue 4, pp. 1039 - 1073
Journal Article
Journal of Computational Information Systems, ISSN 1553-9105, 12/2011, Volume 7, Issue 13, pp. 4660 - 4667
Journal Article
Izvestiya: Mathematics, ISSN 1064-5632, 10/2007, Volume 71, Issue 5, pp. 895 - 938
We obtain upper and lower bounds for the best accuracy of approximation in Stechkin's problem for the differentiation operator and in the problem of the... 
BOUNDED OPERATORS | MATHEMATICS | NUMBER | VALUES | FINITELY SMOOTH FUNCTIONS | POINTS
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 2/2009, Volume 25, Issue 2, pp. 279 - 286
Journal Article
Journal of Complexity, ISSN 0885-064X, 06/2008, Volume 24, Issue 3, pp. 398 - 409
We study the information-based complexity of the approximation problem on the multivariate Sobolev space with bounded mixed derivative MWp,αr in the norm of Lq... 
Monte Carlo method | Sobolev space with bounded mixed derivative | Asymptotic order | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | asymptotic order | Analysis | Methods
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2016, Volume 54, Issue 2, pp. 1056 - 1084
We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann... 
Domain derivative | Duality | Shape functionals | Infimum problems | MATHEMATICS, APPLIED | CONVEXITY | domain derivative | POSITIVE SOLUTIONS | infimum problems | EQUATIONS | PRINCIPLE | shape functionals | duality | SOBOLEV SPACES | SYMMETRY | BOUNDED SLOPE CONDITION | REGULARITY | OPTIMIZATION | FUNCTIONALS | AUTOMATION & CONTROL SYSTEMS | Mathematics - Optimization and Control | Mathematics
Journal Article
Constructive Approximation, ISSN 0176-4276, 11/2006, Volume 24, Issue 3, pp. 245 - 262
In this paper, we determine the asymptotic values of the probabilistic adaptive widths of the space of multivariate functions with bounded mixed derivative... 
Average adaptive width | Sobolev space with bounded mixed derivative | Gaussian measure | Analysis | Numerical Analysis | Probabilistic adaptive width | Mathematics | MATHEMATICS | probabilistic adaptive width | average adaptive width | APPROXIMATION
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 2005, Volume 132, Issue 1, pp. 77 - 96
We determine the asymptotic values on the linear probabilistic ( N , δ ) -widths and linear p-average N-widths of the space of multivariate functions with... 
Probabilistic linear width | Sobolev space with bounded mixed derivative | Gaussian measure | Average linear width | MATHEMATICS | SMOOTH FUNCTIONS | APPROXIMATION | average linear width | probabilistic linear width
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 09/2017, Volume 345, pp. 74 - 90
Journal Article
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 1072-6691, 08/2015, Volume 2015, Issue 201, pp. 1 - 18
We study a class of nonlinear partial differential equations, which can be connected with wave-type equations and Laplace-type equations, by using a... 
MATHEMATICS | MATHEMATICS, APPLIED | bounded solution | WAVES | Analytic solution | PDE with mixed derivatives | wave-type PDE | sine-Gordon | series solution | Klein-Gordon | SYSTEMS | Laplace-type PDE
Journal Article
Kyushu Journal of Mathematics, ISSN 1340-6116, 2017, Volume 71, Issue 1, pp. 31 - 64
We consider a nonsingular transformation whose Perron-Frobenius operator is quasi-compact on an appropriate Banach algebra. We establish the central limit... 
central limit theorem of mixed type | perturbed Perron-Frobenius operator | Central limit theorem of mixed type | Perturbed Perron–Frobenius operator | MATHEMATICS | INVARIANT-MEASURES | PIECEWISE MONOTONIC TRANSFORMATIONS | ERGODIC PROPERTIES | BOUNDED VARIATION
Journal Article
Houston Journal of Mathematics, ISSN 0362-1588, 2007, Volume 33, Issue 3, pp. 927 - 939
We study the continuity of functions u whose mixed derivative partial derivative 1...partial derivative(Nu) is a measure. If u epsilon W-1,W-1(R-N), then we... 
Functions whose derivatives are measures | Functions of bounded variation | Sobolev spaces | Embedding theorems | Continuous functions | MATHEMATICS | functions of bounded variation | embedding theorems | continuous functions | functions whose derivatives axe measures
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2007, Volume 359, Issue 5, pp. 2443 - 2461
We prove that if f:I\subset \mathbb{R}\to \mathbb{R} is of bounded variation, then the uncentered maximal function Mf is absolutely continuous, and its... 
Open intervals | Mathematical intervals | Mathematical theorems | Interior points | Eigenfunctions | Mathematical functions | Mathematical inequalities | Sobolev spaces | Continuous functions | Functions of bounded variation | Maximal function | MATHEMATICS | functions of bounded variation | maximal function | SOBOLEV SPACES
Journal Article
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, ISSN 0232-2064, 2007, Volume 26, Issue 4, pp. 473 - 480
In this note we prove that a harmonic function u on the unit ball B subset of R-n belongs to the harmonic mixed norm space A(s)(p,q) (B), when p,q is an... 
MATHEMATICS, APPLIED | unit ball | POLYDISK | harmonic function | HL-property | WEIGHTED INTEGRALS | mixed norm space | MATHEMATICS | BOUNDED SYMMETRIC DOMAINS | BLOCH SPACE | HOLOMORPHIC-FUNCTIONS | VARIABLES | DERIVATIVES | BERGMAN SPACES
Journal Article
Mathematical Notes, ISSN 0001-4346, 9/1999, Volume 66, Issue 3, pp. 261 - 270
The paper deals with approximations of functions with bounded mixed difference by Haar polynomials. Approximations of the following two different types are... 
Haar polynomial | function with bounded mixed derivative or difference | Mathematics, general | Mathematics | approximation of functions | the best approximation | Banach space | the best m -term approximation
Journal Article
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