What question did this study set out to answer?

The aim is to establish a Fredholm criterion for Wiener–Hopf operators within specific functional spaces.

May 29, 2026

Fredholm criteria for the algebra generated by Wiener–Hopf operators with continuous symbols

MVMárcio ValenteUniversidade Nova de Lisboa

Key Points

The aim is to establish a Fredholm criterion for Wiener–Hopf operators within specific functional spaces.
Examine operators within Banach algebra generated by Wiener–Hopf operators.
Focus on continuous symbols in Lorentz spaces and reflexive Orlicz spaces.
A clear criterion is established linking the properties of the operators to their functional space behavior.
Demonstrates applicability in different types of space, enhancing the understanding of operator theory.

Abstract

Abstract Let X ⁢ (ℝ +) X (R+) be a Lorentz space L p, q ⁢ (ℝ +) L^{p, q (R+) } with 1 p, q ∞ 1 L Φ ⁢ (ℝ +) {L^{ (R+) }. We establish a Fredholm criterion for operators from the Banach algebra generated by all Wiener–Hopf operators with continuous symbols on the space X ⁢ (ℝ +) X (R+).

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