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Fourier expansion along geodesics on Riemann surfaces

100%

Deitmar A.

Open Mathematics

2014

tom 12

nr 4

559-573

For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.

Under which conditions is the Jacobi space $$L_{w^{(a,b)} }^p [ - 1,1]$$ subset of $$L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]$$ ?

88%

Felten M.

Open Mathematics

2007

tom 5

nr 3

505-511

Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property $$L_{w^{(a,b)} }^p [ - 1,1]$$ ⊂ $$L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]$$ is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.

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2 Open Mathematics

1 Deitmar A.

1 Felten M.

1 2014

1 2007

Wyniki wyszukiwania

Fourier expansion along geodesics on Riemann surfaces

Under which conditions is the Jacobi space $$L_{w^{(a,b)} }^p [ - 1,1]$$ subset of $$L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]$$ ?