Eigenvalues of K-invariant Toeplitz Operators on Bounded Symmetric Domains

Abstract

Abstract We determine the eigenvalues of certain “fundamental” K -invariant Toeplitz type operators on weighted Bergman spaces over bounded symmetric domains $$D=G/K,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math> for the irreducible K -types indexed by all partitions of length $$r={\mathrm {rank}}(D)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>rank</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> .

Locations

• Integral Equations and Operator Theory - View - PDF