OOIR: Observatory of International Research

Papers

(The median citation count of Constructive Approximation is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-11-01 to 2024-11-01.)

Article	Citations
Nonlinear Approximation and (Deep) $$\mathrm {ReLU}$$ Networks	91
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs	65
Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series	51
DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing	42
The Barron Space and the Flow-Induced Function Spaces for Neural Network Models	35
Approximation Spaces of Deep Neural Networks	35
Exponential ReLU DNN Expression of Holomorphic Maps in High Dimension	28
Universal Approximations of Invariant Maps by Neural Networks	27
Worst-case Recovery Guarantees for Least Squares Approximation Using Random Samples	24
Sampling Discretization of Integral Norms	16
Semi-algebraic Approximation Using Christoffel–Darboux Kernel	14
Analysis of Target Data-Dependent Greedy Kernel Algorithms: Convergence Rates for f-, $$f \cdot P$$- and f/P-Greedy	13
Wiener Algebras and Trigonometric Series in a Coordinated Fashion	11
Optimal Sampling and Christoffel Functions on General Domains	8
On the Value-Distribution of Hurwitz Zeta-Functions with Algebraic Parameter	8
Strong Partially Greedy Bases and Lebesgue-Type Inequalities	7
Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case	7
Bidemocratic Bases and Their Connections with Other Greedy-Type Bases	6
Set-Valued $$\alpha $$-Fractal Functions	6
A Vector Equilibrium Problem for Symmetrically Located Point Charges on a Sphere	6
Sampling Discretization of the Uniform Norm	6
Sparse Approximation of Triangular Transports, Part I: The Finite-Dimensional Case	5
A Newman type bound for $$L_p[-1,1]$$-means of the logarithmic derivative of polynomials having all zeros on the unit circle	5
Graph Recovery from Incomplete Moment Information	5
Universal Sampling Discretization	5

Riesz Energy Problems with External Fields and Related Theory	5
Large-Degree Asymptotics of Rational Painlevé-IV Solutions by the Isomonodromy Method	5
Orthogonal Polynomials with Ultra-Exponential Weight Functions: An Explicit Solution to the Ditkin–Prudnikov Problem	4
Robust and Resource-Efficient Identification of Two Hidden Layer Neural Networks	4
Optimal Recovery from Inaccurate Data in Hilbert Spaces: Regularize, But What of the Parameter?	4
Characterization of the Variation Spaces Corresponding to Shallow Neural Networks	4
Constructive Approximation on Graded Meshes for the Integral Fractional Laplacian	4
Discrepancy of Minimal Riesz Energy Points	3
Extension Operators for Some Ultraholomorphic Classes Defined by Sequences of Rapid Growth	3
Discrete Self-adjoint Dirac Systems: Asymptotic Relations, Weyl Functions and Toeplitz Matrices	3
Lipschitz Widths	3
Nonnegative and Strictly Positive Linearization of Jacobi and Generalized Chebyshev Polynomials	3
Fourier Interpolation with Zeros of Zeta and L-Functions	3
Depth Separations in Neural Networks: What is Actually Being Separated?	2
Coconvex Approximation of Periodic Functions	2
A Lower Bound for the Logarithmic Energy on $$\mathbb {S}^2$$ and for the Green Energy on $$\mathbb {S}^n$$	2
Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points	2
On the Omnipresence of Spurious Local Minima in Certain Neural Network Training Problems	2
Neural Network Identifiability for a Family of Sigmoidal Nonlinearities	2
The Spectrality of Self-affine Measure Under the Similar Transformation of $$GL_n(p)$$	2
Multivariate Generalized Hermite Subdivision Schemes	2
Approximation and Localized Polynomial Frame on Double Hyperbolic and Conic Domains	2
Cyclic Pólya Ensembles on the Unitary Matrices and their Spectral Statistics	2
Analysis of a Stabilised Finite Element Method for Power-Law Fluids	2
The Product of m Real $$N\times N$$ Ginibre Matrices: Real Eigenvalues in the Critical Regime $$m=O(N)$$	2
Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents	2
Universal Regular Conditional Distributions via Probabilistic Transformers	2
Min-Max Polarization for Certain Classes of Sharp Configurations on the Sphere	2
Computation of Power Law Equilibrium Measures on Balls of Arbitrary Dimension	2
Markov’s Theorem for Weight Functions on the Unit Circle	2
Fourier Multipliers on a Vector-Valued Function Space	2
An Embedding of ReLU Networks and an Analysis of Their Identifiability	2
Variable Anisotropic Singular Integral Operators	2
Phase Retrieval by Binary Questions: Which Complementary Subspace is Closer?	2
Spectral Decomposition of Discrepancy Kernels on the Euclidean Ball, the Special Orthogonal Group, and the Grassmannian Manifold	2
Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality	2
Approximation of Wave Packets on the Real Line	2
Fast and Stable Approximation of Analytic Functions from Equispaced Samples via Polynomial Frames	2
Strong Asymptotic of Cauchy Biorthogonal Polynomials and Orthogonal Polynomials with Varying Measure	1
Construction of Nonlinear Approximation Schemes for Piecewise Smooth Data	1
Compactly-Supported Isotropic Covariances on Spheres Obtained from Matrix-Valued Covariances in Euclidean Spaces	1
Failure of Approximation of Odd Functions by Odd Polynomials	1
Optimal Polynomial Prediction Measures and Extremal Polynomial Growth	1
Radial Basis Function Approximation with Distributively Stored Data on Spheres	1
Applications of the Lipschitz Summation Formula and a Generalization of Raabe’s Cosine Transform	1
Unregularized Online Algorithms with Varying Gaussians	1
Wall Polynomials on the Real Line: A Classical Approach to OPRL Khrushchev’s Formula	1
Complete Minimal Logarithmic Energy Asymptotics for Points in a Compact Interval: A Consequence of the Discriminant of Jacobi Polynomials	1
The Complete Asymptotic Evaluation for Mellin Convolution Operators	1
On the Algebraic Difference Independence of the Euler Gamma Function $$\Gamma $$ and Dirichlet Series	1

Sparse Estimation: An MMSE Approach	1
Component-by-Component Digit-by-Digit Construction of Good Polynomial Lattice Rules in Weighted Walsh Spaces	1
Properties of Vector-Valued $$\tau $$-Discrete Fractional Calculus and its Connection with Caputo Fractional Derivatives	1
Correction to: Wiener Algebras and Trigonometric Series in a Coordinated Fashion	1
Uniform Asymptotic Expansions for Gegenbauer Polynomials and Related Functions via Differential Equations Having a Simple Pole	1
Wiener–Hopf Difference Equations and Semi-Cardinal Interpolation with Integrable Convolution Kernels	1
Wiman–Valiron Theory for a Polynomial Series Based on the Askey–Wilson Operator	1
On the Sparsity of LASSO Minimizers in Sparse Data Recovery	1
Approximation with One-Bit Polynomials in Bernstein Form	1
Path Regularity of the Brownian Motion and the Brownian Sheet	1
Polynomial Approximation of Piecewise Analytic Functions on Quasi-Smooth Arcs	1
Numerical Integration and Discrepancy Under Smoothness Assumption and Without It	1
Minimum Energy Problems with External Fields on Locally Compact Spaces	1
Sharp Constants of Approximation Theory: VI. Weighted Polynomial Inequalities of Different Metrics on the Multidimensional Cube and Ball	1
Duals of Besov and Triebel-Lizorkin Spaces Associated with Operators	1
The spherical ensemble and quasi-Monte-Carlo designs	1
Rodrigues’ Descendants of a Polynomial and Boutroux Curves	1
On the Connection Problem for the Second Painlevé Equation with Large Initial Data	1
Loewner Theory for Bernstein Functions I: Evolution Families and Differential Equations	1
Modulated Bi-Orthogonal Polynomials on the Unit Circle: The $$2j-k$$ and $$j-2k$$ Systems	1
Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials	1
Quantization for Spectral Super-Resolution	1
Cyclic Polynomials in Dirichlet-Type Spaces in the Unit Ball of $${\mathbb {C}}^2$$	1
Orthogonal Polynomials with Periodically Modulated Recurrence Coefficients in the Jordan Block Case II	1
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions	1
Duality and Difference Operators for Matrix Valued Discrete Polynomials on the Nonnegative Integers	1