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Boundedness of propagators for Dirac equations with potentials on Wiener amalgam spaces

Shun Takizawa

Abstract

In this paper we prove boundedness of propagators for Dirac equations with unbounded time-dependent potentials on Wiener amalgam spaces. In particular we deal with class of potentials such as including Stark and harmonic potentials.

Boundedness of propagators for Dirac equations with potentials on Wiener amalgam spaces

Abstract

In this paper we prove boundedness of propagators for Dirac equations with unbounded time-dependent potentials on Wiener amalgam spaces. In particular we deal with class of potentials such as including Stark and harmonic potentials.

Paper Structure

This paper contains 10 sections, 69 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Short-time Fourier transform (STFT)
  5. Modulation and Wiener amalgam spaces
  6. Proof of Theorem \ref{['thm1']}
  7. Construction of a parametrix
  8. Proof of boundedness of operators
  9. Proof of well-posedness
  10. Proof of Theorem \ref{['thm2']}

Theorems & Definitions (1)

  • proof