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Unbounded integral Hankel operators

Alexander Pushnitski, Sergei Treil

Abstract

For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.

Unbounded integral Hankel operators

Abstract

For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.

Paper Structure

This paper contains 44 sections, 148 equations.

Table of Contents

  1. Introduction
  2. Foreword
  3. Hankel operators: discrete and continuous realisations
  4. Positive semi-definite Hankel matrices: the quadratic form of $\gamma_\mu$
  5. Operator domains: the case $h\in\ell^2$
  6. Generalisation to the non-self-adjoint case
  7. Operator domains: the case $h\notin\ell^2$
  8. Main results
  9. Integral Hankel operators
  10. The quadratic form of $\Gamma_\mu$
  11. Operator domains: $h_\mu$ is square integrable at infinity
  12. Generalisation to the non-self-adjoint case
  13. Domains: general case
  14. The kernel of $\Gamma_\mu$
  15. Dictionary
  16. ...and 29 more sections

Theorems & Definitions (8)

  • proof
  • proof
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