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 2020-03-01 to 2024-03-01.)

Article	Citations
Nonlinear Approximation and (Deep) $$\mathrm {ReLU}$$ Networks	59
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs	53
Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series	45
DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing	35
Approximation Spaces of Deep Neural Networks	31
The Barron Space and the Flow-Induced Function Spaces for Neural Network Models	24
Exponential ReLU DNN Expression of Holomorphic Maps in High Dimension	21
Universal Approximations of Invariant Maps by Neural Networks	20
Worst-case Recovery Guarantees for Least Squares Approximation Using Random Samples	19
Sampling Discretization of Integral Norms	16
Wiener Algebras and Trigonometric Series in a Coordinated Fashion	10
Analysis of Target Data-Dependent Greedy Kernel Algorithms: Convergence Rates for f-, $$f \cdot P$$- and f/P-Greedy	9
Semi-algebraic Approximation Using Christoffel–Darboux Kernel	7
Optimal Sampling and Christoffel Functions on General Domains	7
Strong Partially Greedy Bases and Lebesgue-Type Inequalities	6
On the Value-Distribution of Hurwitz Zeta-Functions with Algebraic Parameter	6
Approximation to uniform distribution in $$\mathrm {SO}(3)$$	6
Turán-Type Reverse Markov Inequalities for Polynomials with Restricted Zeros	6
Riesz Energy Problems with External Fields and Related Theory	5
Boundary Behavior of Optimal Polynomial Approximants	5
Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case	5
A Vector Equilibrium Problem for Symmetrically Located Point Charges on a Sphere	5
Entropy Numbers of Finite Dimensional Mixed-Norm Balls and Function Space Embeddings with Small Mixed Smoothness	5
Polynomial Approximation of Anisotropic Analytic Functions of Several Variables	5
Orthogonal Polynomials with Ultra-Exponential Weight Functions: An Explicit Solution to the Ditkin–Prudnikov Problem	4

Bidemocratic Bases and Their Connections with Other Greedy-Type Bases	4
Characterization of the Variation Spaces Corresponding to Shallow Neural Networks	4
Robust and Resource-Efficient Identification of Two Hidden Layer Neural Networks	4
Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges	4
Set-Valued $$\alpha $$-Fractal Functions	4
Large-Degree Asymptotics of Rational Painlevé-IV Solutions by the Isomonodromy Method	4
Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I	3
Sparse Approximation of Triangular Transports, Part I: The Finite-Dimensional Case	3
Planar Sampling Sets for the Short-Time Fourier Transform	3
Discrepancy of Minimal Riesz Energy Points	3
Zero Distribution of Orthogonal Polynomials on a q-Lattice	3
Optimal Recovery from Inaccurate Data in Hilbert Spaces: Regularize, But What of the Parameter?	3
Ambient Approximation on Embedded Submanifolds	3
Fourier Interpolation with Zeros of Zeta and L-Functions	3
Fast and Stable Approximation of Analytic Functions from Equispaced Samples via Polynomial Frames	2
Sampling Discretization of the Uniform Norm	2
Phase Retrieval by Binary Questions: Which Complementary Subspace is Closer?	2
Neural Network Identifiability for a Family of Sigmoidal Nonlinearities	2
Approximation of Wave Packets on the Real Line	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
Rational Minimax Iterations for Computing the Matrix pth Root	2
Fourier Multipliers on a Vector-Valued Function Space	2
Constructive Approximation on Graded Meshes for the Integral Fractional Laplacian	2
Cyclic Polynomials in Dirichlet-Type Spaces in the Unit Ball of $${\mathbb {C}}^2$$	2
Variable Besov Spaces Associated with Heat Kernels	2
Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality	2
Discrete Self-adjoint Dirac Systems: Asymptotic Relations, Weyl Functions and Toeplitz Matrices	2
Gegenbauer and Other Planar Orthogonal Polynomials on an Ellipse in the Complex Plane	2
Variable Anisotropic Singular Integral Operators	2
Distortion and Critical Values of the Finite Blaschke Product	2
Universal Sampling Discretization	2
Universal Regular Conditional Distributions via Probabilistic Transformers	2
The Spectrality of Self-affine Measure Under the Similar Transformation of $$GL_n(p)$$	2
Hyperuniform Point Sets on Flat Tori: Deterministic and Probabilistic Aspects	2
Numerical Integration and Discrepancy Under Smoothness Assumption and Without It	1
Sharp Constants of Approximation Theory: VI. Weighted Polynomial Inequalities of Different Metrics on the Multidimensional Cube and Ball	1
Multivariate Generalized Hermite Subdivision Schemes	1
Applications of the Lipschitz Summation Formula and a Generalization of Raabe’s Cosine Transform	1
Construction of Nonlinear Approximation Schemes for Piecewise Smooth Data	1
Hermite-Poulain Theorems for Linear Finite Difference Operators	1
Failure of Approximation of Odd Functions by Odd Polynomials	1
Approximation and Localized Polynomial Frame on Double Hyperbolic and Conic Domains	1
The Product of m Real $$N\times N$$ Ginibre Matrices: Real Eigenvalues in the Critical Regime $$m=O(N)$$	1
Approximation with One-Bit Polynomials in Bernstein Form	1
A Lower Bound for the Logarithmic Energy on $$\mathbb {S}^2$$ and for the Green Energy on $$\mathbb {S}^n$$	1
Path Regularity of the Brownian Motion and the Brownian Sheet	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
Duality and Difference Operators for Matrix Valued Discrete Polynomials on the Nonnegative Integers	1

Duals of Besov and Triebel-Lizorkin Spaces Associated with Operators	1
Lipschitz Widths	1
Coconvex Approximation of Periodic Functions	1
Markov’s Theorem for Weight Functions on the Unit Circle	1
On the Connection Problem for the Second Painlevé Equation with Large Initial Data	1
Depth Separations in Neural Networks: What is Actually Being Separated?	1
Wiener–Hopf Difference Equations and Semi-Cardinal Interpolation with Integrable Convolution Kernels	1
Quantization for Spectral Super-Resolution	1
Analysis of a Stabilised Finite Element Method for Power-Law Fluids	1
On the Sparsity of LASSO Minimizers in Sparse Data Recovery	1
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions	1
Spectral Decomposition of Discrepancy Kernels on the Euclidean Ball, the Special Orthogonal Group, and the Grassmannian Manifold	1
Minimum Energy Problems with External Fields on Locally Compact Spaces	1
Extension Operators for Some Ultraholomorphic Classes Defined by Sequences of Rapid Growth	1
Uniform Asymptotic Expansions for Gegenbauer Polynomials and Related Functions via Differential Equations Having a Simple Pole	1
Strong Asymptotic of Cauchy Biorthogonal Polynomials and Orthogonal Polynomials with Varying Measure	1
Wiman–Valiron Theory for a Polynomial Series Based on the Askey–Wilson Operator	1
Correction to: Wiener Algebras and Trigonometric Series in a Coordinated Fashion	1
Component-by-Component Digit-by-Digit Construction of Good Polynomial Lattice Rules in Weighted Walsh Spaces	1
Optimal Polynomial Prediction Measures and Extremal Polynomial Growth	1
An Embedding of ReLU Networks and an Analysis of Their Identifiability	1
Nonnegative and Strictly Positive Linearization of Jacobi and Generalized Chebyshev Polynomials	1
Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents	1
Orthogonal Polynomials with Periodically Modulated Recurrence Coefficients in the Jordan Block Case II	1
A Newman type bound for $$L_p[-1,1]$$-means of the logarithmic derivative of polynomials having all zeros on the unit circle	1