Toeplitz Operators with Vertical Symbols Acting on the Poly-Bergman Spaces of the Upper Half-Plane. II

2019 ◽  
Vol 13 (5) ◽  
pp. 2443-2462 ◽  
Author(s):  
Josué Ramírez Ortega ◽  
María del Rosario Ramírez Mora ◽  
Armando Sánchez Nungaray
Keyword(s):  
Half Plane ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Upper Half Plane

scholarly journals Toeplitz operators and Wiener-Hopf factorisation: an introduction

2017 ◽  
Vol 4 (1) ◽  
pp. 130-145 ◽  
Author(s):  
M. Cristina Câmara
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Toeplitz Operators ◽  
Sufficient Conditions ◽  
Singular Integral Equations ◽  
Necessary And Sufficient Conditions ◽  
Upper Half Plane ◽  
Necessary And Sufficient

Abstract Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)

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