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A formulation of the Jacobi coefficients clj(a,b)via Bell polynomials
The Jacobi polynomials ( , ) are deeply intertwined with the Laplacian on compact rank one symmetric spaces. They represent the spherical or zonal functions and as such constitute the main ingredients in describing the spectral measures and spectral projections associated with the Laplacian on these spaces. In this note we strengthen this connection by showing that a set of spectral and geometric quantities associated with Jacobi operator fully describe the Maclaurin coefficients associated with the heat and other related Schwartzian kernels and present an explicit formulation of these quantities using the Bell polynomials.
History
Publication status
- Published
File Version
- Published version
Journal
Advances in Operator TheoryISSN
2538-225XPublisher
Tusi Mathematical Research GroupExternal DOI
Issue
4Volume
2Page range
506-515Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes