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Proceedings of the American Mathematical Society, ISSN 0002-9939, 2019, p. 1
Journal Article
Positivity, ISSN 1385-1292, 03/2019
Journal Article
Journal of Complexity, ISSN 0885-064X, 10/2017, Volume 42, pp. 85 - 93
The main result of this paper is a proof that for any integrable function on the torus, any sequence of its orthogonal projections onto periodic spline spaces... 
Almost everywhere convergence | Periodic splines | ARBITRARY KNOTS | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | Projectors | Analysis
Journal Article
Studia Mathematica, ISSN 0039-3223, 2014, Volume 222, Issue 1, pp. 51 - 86
Journal Article
STUDIA MATHEMATICA, ISSN 0039-3223, 2014, Volume 222, Issue 1, pp. 49 - 84
We prove that given any natural number k and any dense point sequence (t(n)), the corresponding orthonormal spline system is an unconditional basis in... 
ARBITRARY KNOTS | MATHEMATICS | unconditional basis | orthonormal spline system | PROJECTIONS | L-p | Mathematics - Functional Analysis
Journal Article
Journal of Complexity, ISSN 0885-064X, 10/2019, Volume 54, p. 101409
The irregularities of a distribution of points in the unit interval are often measured with various notions of discrepancy. The discrepancy function can be... 
Discrepancy function | Convolution inequalities | MATHEMATICS | MATHEMATICS, APPLIED | POINT SETS
Journal Article
STUDIA MATHEMATICA, ISSN 0039-3223, 2019, Volume 248, Issue 1, pp. 57 - 91
Given any natural number k and any dense point sequence (t(n)) on the torus T, we prove that the corresponding periodic orthonormal spline system of order k is... 
MATHEMATICS | THEOREM | SPACES | unconditional basis | CONVERGENCE | orthonormal spline system | PROJECTIONS | L-p
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 12/2017, Volume 30, Issue 4, pp. 1445 - 1470
We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis.... 
46B07 | 46B45 | Order statistic | 62G30 | Probability Theory and Stochastic Processes | Embedding | Mathematics | Orlicz space | Statistics, general | SEQUENCES | RECONSTRUCTION | ZONOTOPES | STATISTICS & PROBABILITY | RANDOM-VARIABLES | EMBEDDING SUBSPACES | MUSIELAK-ORLICZ SPACES | MATRICES | COMBINATORIAL | L(P)(N) | PROBABILISTIC INEQUALITIES
Journal Article
MICHIGAN MATHEMATICAL JOURNAL, ISSN 0026-2285, 2019, Volume 68, Issue 1, pp. 3 - 17
Let d is an element of N, and let f be a function in the Orlicz class L(log(+) L)(d-1) defined on the unit cube [0, 1](d) in R-d. Given knot sequences... 
MATHEMATICS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2016, Volume 144, Issue 5, pp. 2133 - 2148
We prove some probabilistic estimates for tensor products of random vectors, generalizing results that were obtained by Gordon, Litvak, Schütt, and Werner... 
Orlicz function | Random vector | Orlicz norm | Tensor product | ORLICZ NORMS | MATHEMATICS, APPLIED | INEQUALITIES | SEQUENCES | random vector | BANACH-SPACE THEORY | RANDOM POLYTOPES | tensor product | RANDOM-VARIABLES | MATHEMATICS | L-1 | COMBINATORIAL | SUBSPACES
Journal Article
Studia Mathematica, ISSN 0039-3223, 2011, Volume 205, Issue 3, pp. 251 - 279
We identify the torus with the unit interval [0,1) and let n, nu is an element of N with 0 <= nu <= n - 1 and N := n + nu. Then we define the (partially... 
Lebesgue constant | Periodic Franklin system | MATHEMATICS | B-SPLINES | THEOREM | periodic Franklin system | Mathematics - Numerical Analysis
Journal Article
12/2013
Bulletin Polish Acad. Sci. Math. 62 (2014), 139-159 In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic... 
Mathematics - Functional Analysis
Journal Article
IEEE Transactions on Control Systems Technology, ISSN 1063-6536, 03/2014, Volume 22, Issue 2, pp. 607 - 617
Hydrodynamic dynamometers are employed in internal combustion engine (ICE) test benches for the entire range of ICEs, from cart engines to large ship engines.... 
torque control | Hydrodynamic dynamometer | inversion of nonlinear static maps | LOOP PERFORMANCE | COMPUTER-SIMULATION | SYSTEMS | ENGINE TEST BENCHES | AUTOMATION & CONTROL SYSTEMS | FILL HYDRAULIC DYNAMOMETER | ENGINEERING, ELECTRICAL & ELECTRONIC | Parametrization | Fluid flow | Hydrodynamics | Nonlinearity | Inverse | Dynamometers | Marine engines | Benches
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 03/2014, Volume 180, Issue 1, pp. 77 - 89
The main result of this paper is a proof that, for any , a sequence of its orthogonal projections onto splines of order with arbitrary knots converges almost... 
Splines | Almost everywhere convergence | Inverse Gram matrix | MATHEMATICS | Mathematics - Functional Analysis
Journal Article
Studia Mathematica, ISSN 0039-3223, 2015, Volume 226, Issue 2, pp. 123 - 154
Journal Article
12/2018
We show that D. L\'{e}pingle's $L_1(\ell_2)$-inequality \begin{equation*} \Big\| \big( \sum_n \mathbb E[f_n | \mathscr F_{n-1}]^2 \big)^{1/2}\Big\|_1 \leq... 
Journal Article
07/2018
We give necessary and sufficient conditions for a Banach space $X$ having the Radon-Nikod\'{y}m property in terms of polynomial spline sequences. 
Mathematics - Functional Analysis
Journal Article
Electronic Communications in Probability, ISSN 1083-589X, 2015, Volume 20, pp. 1 - 12
We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain... 
Order statistic | Combinatorial inequality | Probabilistic inequality | Real interpolation | real interpolation | SEQUENCES | probabilistic inequality | ORLICZ SPACES | COMBINATORIAL | PROBABILISTIC INEQUALITIES | STATISTICS & PROBABILITY | BANACH-SPACE THEORY | combinatorial inequality | RANDOM-VARIABLES | Mathematics - Probability
Journal Article
01/2010
Let (X,d,\mu) be a space of homogeneous type and E a UMD Banach space. Under the assumption mu({x})=0 for all x in X, we prove a representation theorem for... 
Mathematics - Functional Analysis
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2012, Volume 262, Issue 4, pp. 1427 - 1465
Let be a space of homogeneous type. Under the assumption for all , we prove a decomposition theorem for singular integral operators on . Isotropic Haar... 
Martingale transforms | Spaces of homogeneous type | UMD spaces | Rearrangement and shift operators | Singular integral operators | INTERPOLATION | MATHEMATICS | HARDY-SPACES | CALDERON-ZYGMUND OPERATORS
Journal Article
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