OOIR: Observatory of International Research

Papers

(The TQCC of Constructive Approximation is 2. 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
Approximation Spaces of Deep Neural Networks	35
The Barron Space and the Flow-Induced Function Spaces for Neural Network Models	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
Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case	7
Strong Partially Greedy Bases and Lebesgue-Type Inequalities	7
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
Bidemocratic Bases and Their Connections with Other Greedy-Type Bases	6
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

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
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
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
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
Discrepancy of Minimal Riesz Energy Points	3
Extension Operators for Some Ultraholomorphic Classes Defined by Sequences of Rapid Growth	3
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
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