In this paper we study the sampling recovery problem for certain relevant multivariate function classes which are not compactly embedded into $L_\infty$. Recent tools relating the sampling numbers to the Kolmogorov widths in the uniform norm are therefore not applicable. In a sense, we continue the research on the small smoothness problem by considering "very" small smoothness in the context of Besov and Triebel-Lizorkin spaces with dominating mixed regularity. There is not much known on the recovery of such functions except of an old result by Oswald in the univariate situation. As a first step we prove the uniform boundedness of the $\ell_p$-norm of the Faber-Schauder coefficients in a fixed level. Using this we are able to control the er...
AbstractAn abstract form of the classical approximate sampling theorem is proved for functions on a ...
In this thesis we study different variations of sampling inequalities. First,mirroring a result in [...
AbstractBeurling–Landau-type results are known for a rather small class of functions limited to the ...
We study the recovery of functions in the uniform norm based on function evaluations. We obtain wors...
For multivariate Besov-type classes $U^a_{p,\theta}$ of functions having nonuniform mixed smoothness...
AbstractWe present a new approach to the problem of irregular sampling of band-limited functions tha...
It is known that results on universal sampling discretization of the square norm are useful in spars...
summary:Using the techniques of approximation and factorization of convolution operators we study th...
AbstractBand-limited functions f can be recovered from their sampling values (f(xi)) by means of ite...
For a class $F$ of complex-valued functions on a set $D$, we denote by $g_n(F)$ its sampling numbers...
AbstractIn this paper, we obtain some weak asymptotic results for average Kolmogorov σ-width and ave...
AbstractWe want to recover a continuous function f:(0,1)d→C using only its function values. Let us a...
We investigate the rate of convergence in ‖ · |Lp‖, 1 ≤ p ≤ ∞, of the d-dimensional Smolyak algorit...
AbstractThe approximate sampling theorem with its associated aliasing error is due to J.L. Brown (19...
The classical assumption in sampling and spline theories is that the input signal is square-integrab...
AbstractAn abstract form of the classical approximate sampling theorem is proved for functions on a ...
In this thesis we study different variations of sampling inequalities. First,mirroring a result in [...
AbstractBeurling–Landau-type results are known for a rather small class of functions limited to the ...
We study the recovery of functions in the uniform norm based on function evaluations. We obtain wors...
For multivariate Besov-type classes $U^a_{p,\theta}$ of functions having nonuniform mixed smoothness...
AbstractWe present a new approach to the problem of irregular sampling of band-limited functions tha...
It is known that results on universal sampling discretization of the square norm are useful in spars...
summary:Using the techniques of approximation and factorization of convolution operators we study th...
AbstractBand-limited functions f can be recovered from their sampling values (f(xi)) by means of ite...
For a class $F$ of complex-valued functions on a set $D$, we denote by $g_n(F)$ its sampling numbers...
AbstractIn this paper, we obtain some weak asymptotic results for average Kolmogorov σ-width and ave...
AbstractWe want to recover a continuous function f:(0,1)d→C using only its function values. Let us a...
We investigate the rate of convergence in ‖ · |Lp‖, 1 ≤ p ≤ ∞, of the d-dimensional Smolyak algorit...
AbstractThe approximate sampling theorem with its associated aliasing error is due to J.L. Brown (19...
The classical assumption in sampling and spline theories is that the input signal is square-integrab...
AbstractAn abstract form of the classical approximate sampling theorem is proved for functions on a ...
In this thesis we study different variations of sampling inequalities. First,mirroring a result in [...
AbstractBeurling–Landau-type results are known for a rather small class of functions limited to the ...