scientific article

Sergei V. Konyagin, Vladimir N. Temlyakov

Publication date: 16 October 2001

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items

Extensions of democracy-like properties for sequences with gaps, New parameters and Lebesgue-type estimates in greedy approximation, Weak forms of unconditionality of bases in greedy approximation, Approximation by Egyptian fractions and the weak greedy algorithm, New characterizations of the unit vector basis of or, On weighted greedy-type bases, Sparse approximation using new greedy-like bases in superreflexive spaces, Stable decomposition of homogeneous mixed-norm Triebel-Lizorkin spaces, Elton's near unconditionality of bases as a threshold-free form of greediness, Fourier coefficients of functions in power-weighted L₂-spaces and conditionality constants of bases in Banach spaces, Greedy-like bases for sequences with gaps, Lipschitz-free Spaces on Finite Metric Spaces, On the Democracy inequality for Haar systems and some geometric and analytical properties in Herz spaces on dyadic settings, Counterexamples in isometric theory of symmetric and greedy bases, Lorentz spaces and embeddings induced by almost greedy bases in superreflexive Banach spaces, Series with monotone coefficients in the Walsh system, Greedy algorithm for general biorthogonal systems, Greedy algorithms and best $m$-term approximation with respect to biorthogonal systems, Unnamed Item, Characterization of 1-greedy bases, On the boundedness of threshold operators in $L_1[0,1$ with respect to the Haar basis], Embeddings and Lebesgue-type inequalities for the greedy algorithm in Banach spaces, Lorentz spaces and embeddings induced by almost greedy bases in Banach spaces, Lebesgue constants for Chebyshev thresholding greedy algorithms, Lebesgue-type inequalities in greedy approximation, Efficiency of weak greedy algorithms for $m$-term approximations, Frames and non linear approximations in Hilbert spaces, Fundamental functions of almost greedy bases of $L_p$ for $1<p< \infty$, Democracy of shearlet frames with applications, Obituary: Nigel John Kalton, 1946-2010, Lebesgue inequalities for the greedy algorithm in general bases, Lebesgue-type inequalities for quasi-greedy bases, Democratic systems of translates, On the uniform convergence of the greedy algorithm in a generalized Walsh system, Asymptotic greediness of the Haar system in the spaces $L_p[0,1$, $1<p<\infty $], Characterization of 1-quasi-greedy bases, Quantifying democracy of wavelet bases in Lorentz spaces, Weight-almost greedy bases, Approximation with brushlet systems., Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases, Greedy bases in weighted modulation spaces, Greedy approximation with regard to non-greedy bases, Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system, Universal functions in `correction' problems guaranteeing the convergence of Fourier-Walsh series, Extensions and new characterizations of some greedy-type bases, On the $L^p$-greedy universal functions with respect to the generalized Walsh system, Lebesgue inequalities for Chebyshev thresholding greedy algorithms, Sparse Approximation by Greedy Algorithms, Best approximation with wavelets in weighted Orlicz spaces, Bidemocratic bases and their connections with other greedy-type bases, Performance of the thresholding greedy algorithm with larger greedy sums, Building highly conditional almost greedy and quasi-greedy bases in Banach spaces, On a greedy algorithm in $L^{1}(0, 1)$ with regard to subsystems of the Haar system and on $\omega $-quasigreedy bases, Greedy bases in $L^p$ spaces, Renorming spaces with greedy bases, Nonlinear approximation by renormalized trigonometric system, On the greedy algorithm by the Haar system, On greedy algorithm in $L^{1}(0, 1)$ by regular Haar system, Quasi-greedy bases in $\ell_p$ ($0 < p < 1$) are democratic, On certain subspaces of $\ell_p$ for $0 < p \le 1$ and their applications to conditional quasi-greedy bases in $p$-Banach spaces, Wavelets and bidemocratic pairs in weighted norm spaces, On the convergence of a weak greedy algorithm for the multivariate Haar basis, On the Convergence of a Greedy Algorithm for the Solution of the Problem for the Construction of Monotone Regression, An example of an almost greedy basis in 𝐿¹(0,1), On rearranged series by Haar system, Divergence of the greedy algorithm in the Faber-Schauder system on a continuum cardinality set, On series by Haar system, Convergence of greedy algorithm in Walsh system in $L_p$, Characterization of greedy bases in Banach spaces, Characterization of 1-almost greedy bases, Wavelets, Orlicz spaces, and greedy bases, The best $m$-term approximation with respect to polynomials with constant coefficients, Conditional quasi-greedy bases in non-superreflexive Banach spaces, An example of an almost greedy uniformly bounded orthonormal basis for $L_p(0,1)$, Equivalence of Haar bases associated with different dyadic systems, Characterizations of democratic systems of translates on locally compact abelian groups, Democracy functions and optimal embeddings for approximation spaces, Orthonormal bases for $\alpha$-modulation spaces, Wavelet bases in the Lebesgue spaces on the field of $p$-adic numbers, No greedy bases for matrix spaces with mixed $\ell_p$ and $\ell_q$ norms, Trigonometric quasi-greedy bases for $L^p(\mathbf T;w)$, Quasi-greedy bases for sequences with gaps, Simultaneous approximation by greedy algorithms, Greedy bases for Besov spaces, Renormings and symmetry properties of 1-greedy bases, Trigonometric bases for matrix weighted $L_p$-spaces, On Faber-Schauder coefficients of continuous functions and divergence of greedy algorithm, Quasi-greedy systems of integer translates, Weight-partially greedy bases and weight-property $(A)$, On the quasi-greedy constant of the Haar subsystems in $L^1(0, 1)$, Characterization of weight-semi-greedy bases, Equivalence between almost-greedy and semi-greedy bases, Banach spaces with a unique greedy basis, The strong $L^{1}$- greedy property of the Walsh system, On left democracy function, Almost isometric constants for partial unconditionality, Results on Non-linear Approximation for Wavelet Bases in Weighted Function Spaces, A note on partially-greedy bases in quasi-Banach spaces, Wavelet approximation of distributions with bounded variation derivatives, Coefficient quantization in Banach spaces, Strong partially greedy bases and Lebesgue-type inequalities, A remark on approximation with polynomials and greedy bases, The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis, Greedy bases are best for $m$-term approximation, Greedy approximation for biorthogonal systems in quasi-Banach spaces, On convergence of weak thresholding greedy algorithm in $L^{1}$(0,1), Wavelet bases in the weighted Besov and Triebel-Lizorkin spaces with $A_p^{\text{loc}}$-weights, The weighted property (A) and the greedy algorithm, Duality gap estimates for weak Chebyshev greedy algorithms in Banach spaces, On the permutative equivalence of squares of unconditional bases, Subsequences of the Haar basis consisting of full levels in $H{\textunderscore }p$ for $0 < p < \infty $, On some characterizations of greedy-type bases, Lebesgue constants for the weak greedy algorithm, Universal bases and greedy algorithms for anisotropic function classes, On approximate $\ell_1$ systems in Banach spaces, Greedy bases in variable Lebesgue spaces, Duality gap estimates for a class of greedy optimization algorithms in Banach spaces, Democratic subsystems of the multiple Haar system, SPARSE APPROXIMATION AND RECOVERY BY GREEDY ALGORITHMS IN BANACH SPACES