Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols

2024/04/22 by Quiroga-Barranco, Raul, Sanchez-Nungaray, Armando
#32A36 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47B35 #Secondary 53D20

paper · doi:10.48550/arxiv.2404.14582

Abstract

For \mathbbBⁿ the n-dimensional unit ball and D_n its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant under the actions of the maximal Abelian subgroups of biholomorphisms \mathbbTⁿ (quasi-elliptic) and \mathbbTⁿ × ℝ₊ (quasi-hyperbolic). Using geometric symplectic tools (Hamiltonian actions and moment maps) we obtain simple diagonalizing spectral integral formulas for such kinds of operators. Some consequences show how powerful the use of our differential geometric methods are.

Related

• Moment maps of Abelian groups and commuting Toeplitz operators acting on\n the unit ball
• Commuting Toeplitz operators and moment maps on Cartan domains of type III
• Toeplitz operators, mathbbT^m-invariance and quasi-homogeneous\n symbols
• The Restriction Principle and Commuting Families of Toeplitz Operators on the Unit Ball
• Radial Toeplitz operators on the weighted Bergman spaces of Cartan\n domains