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Essential sets for random operators constructed from Arratia flow

Andrey Dorogovtsev, Iaroslava Korenovska

Abstract

In this paper we consider a strong random operator $T_t$ which describes shift of functions from $L_2(\mathbb{R})$ along an Arratia flow. We find a compact set in $L_2(\mathbb{R})$ that doesn't disappear under $T_t$, and estimate its Kolmogorov widths.

Essential sets for random operators constructed from Arratia flow

Abstract

In this paper we consider a strong random operator which describes shift of functions from along an Arratia flow. We find a compact set in that doesn't disappear under , and estimate its Kolmogorov widths.

Paper Structure

This paper contains 4 sections, 8 theorems, 77 equations.

Table of Contents

  1. Introduction. Arratia flow and random operators
  2. $T_t$-essential functions
  3. On change of compact sets under strong random operator generated by an Arratia flow
  4. On subspace that preserves dimension under random operator generated by an Arratia flow

Key Result

Theorem \oldthetheorem

For any time $t>0$ and nonnegative measurable function $h:\mathbb{R}\to\mathbb{R}$ such that $\int_{\mathbb{R}}h(u)du<+\infty$ where the last integral is in scence of Lebesgue-Stieltjes.

Theorems & Definitions (19)

  • Definition \oldthetheorem: 1
  • Theorem \oldthetheorem: 2
  • Definition \oldthetheorem
  • Example \oldthetheorem
  • Theorem \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • proof
  • ...and 9 more