## 9 Citations

### Some improved bounds in sampling discretization of integral norms

- Mathematics, Computer ScienceArXiv
- 2022

This paper proves sampling discretization results under a standard assumption formulated in terms of the Nikol’skii-type inequality, and obtains some upper bounds on the number of sam-ple points suﬃcient for good discretized of the integral L p norms of functions from ﬁnite-dimensional subspaces of continuous functions.

### Randomized weakly admissible meshes

- Mathematics, Computer ScienceJournal of Approximation Theory
- 2022

### On the reconstruction of functions from values at subsampled quadrature points

- Computer Science, Mathematics
- 2022

The subsampling procedure consists of a computationally inexpensive random step followed by a deterministic procedure to further reduce the number of points while keeping its information, and regains the optimal rate since many of the lattice points are not needed.

### $\varepsilon$-isometric dimension reduction for incompressible subsets of $\ell_p$

- Mathematics, Computer Science
- 2021

Fix p ∈ [1,∞), K ∈ (0,∞) and a probability measure μ. We prove that for every n ∈N, ε ∈ (0,1) and x1, . . . ,xn ∈ Lp(μ) with ∥∥∥maxi∈{1,...,n} |xi |∥∥∥Lp(μ) ≤ K , there exists d ≤ 32e2(2K)2p logn ε2…

### Stable phase retrieval in function spaces

- Mathematics
- 2022

Let (Ω,Σ, μ) be a measure space, and 1 ≤ p ≤ ∞. A subspace E ⊆ Lp(μ) is said to do stable phase retrieval (SPR) if there exists a constant C ≥ 1 such that for any f, g ∈ E we have (0.1) inf |λ|=1 ‖f…

### Marcinkiewicz-Zygmund inequalities for polynomials in Fock space

- MathematicsMathematische Zeitschrift
- 2022

We study the relation between Marcinkiewicz-Zygmund families for polynomials in a weighted L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

### Энтропия унитарного оператора на $L^2(\mathbb T^n)$

- Математический сборник
- 2022

В работе изучается понятие $\mu$-нормы оператора, введенное Д. В. Трещeвым. Мы концентрируемся на случае операторов на пространстве $L^2(\mathbb{T}^n)$, где $\mathbb{T}^n$ - $n$-мерный тор (случай…

### High-Dimensional Geometric Streaming in Polynomial Space

- Computer ScienceArXiv
- 2022

The techniques provide a novel connection between leverage scores, a fundamental object in numerical linear algebra, and computational geometry, and yield nearly optimal trade-oﬀs between space and distortion for ℓ p subspace embeddings.

## References

SHOWING 1-10 OF 154 REFERENCES

### Sampling Discretization of Integral Norms

- Mathematics, Computer ScienceConstructive Approximation
- 2021

A conditional theorem for all integral norms Lq is obtained and a new Marcinkiewicz-type discretization for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses is derived.

### Integral norm discretization and related problems

- MathematicsRussian Mathematical Surveys
- 2019

The problem is discussed of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure. This problem is investigated…

### Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials

- Mathematics, Computer ScienceArXiv
- 2020

It is shown that recently developed techniques allow for a new Marcinkiewicz type discretization theorem for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses.

### Sampling discretization error of integral norms for function classes

- Computer Science, MathematicsJ. Complex.
- 2019

### The Marcinkiewicz-Type Discretization Theorems

- Mathematics, Computer ScienceConstructive Approximation
- 2018

A new technique is presented, which works well for discretization of the integral norm, which is a combination of probabilistic technique, based on chaining, and results on the entropy numbers in the uniform norm.

### A remark on discretization of the uniform norm

- Mathematics, Computer ScienceArXiv
- 2021

A general result is proved, which connects the upper bound on the number of sampling points in the discretization theorem for the uniform norm with the best m-term bilinear approximation of the Dirichlet kernel associated with the given subspace.

### A note on sampling recovery of multivariate functions in the uniform norm

- MathematicsSIAM J. Numer. Anal.
- 2022

The recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm is studied to obtain preasymptotic estimates for the corresponding sampling numbers and a relation to the corresponding Kolmogorov numbers is pointed out.

### L2-norm sampling discretization and recovery of functions from RKHS with finite trace

- Mathematics, Computer ScienceSampling Theory, Signal Processing, and Data Analysis
- 2021

A spectral norm concentration inequality for infinite random matrices with independent rows for L_2-norm sampling discretization and recovery of functions in RKHS based on random function samples, where the kernel is assumed to be the finite trace of the kernel.

### Hyperbolic Cross Approximation

- Computer Science
- 2018

A survey on classical methods developed in multivariate approximation theory, which are known to work very well for moderate dimensions and which have potential for applications in really high dimensions.