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Schur analysis over the unit spectral ball

Daniel Alpay, Ilwoo Cho

Abstract

We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of hypercomplex numbers.

Schur analysis over the unit spectral ball

Abstract

We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of hypercomplex numbers.
Paper Structure (24 sections, 51 theorems, 336 equations)

This paper contains 24 sections, 51 theorems, 336 equations.

Table of Contents

  1. Introduction
  2. Generalities and first examples
  3. Preliminary results
  4. The Fock space
  5. Wiener algebra
  6. Rational functions
  7. The Hardy space
  8. Definition
  9. Resolvent operators and resolvent equations
  10. Blaschke factor
  11. A Beurling-Lax type theorem
  12. Interpolation
  13. Schur multipliers
  14. Definition
  15. Leech Theorem
  16. ...and 9 more sections

Key Result

Proposition 2.2

For any $A\in\mathbb C^{p\times p}$ with $\rho(A)<R$, the series converges absolutely.

Theorems & Definitions (117)

  • Definition 2.1
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Corollary 2.4
  • proof
  • Remark 2.5
  • Proposition 2.6
  • proof
  • ...and 107 more