The eigen functions of the complex projective space
Copyright policy )The eigen functions of the complex projective space
Let \(\lambda_0=0\leq \lambda_1\leq\ldots\leq \lambda_p\leq\dots,\) be the eigenvalues of the Laplace-Beltrami operator on complex projective space \(\mathbb{C} P^n\) and \({\mathcal H}_p\) be the space of eigenvectors corresponding to \(\lambda_p\). In the paper under review, the reproducing kernel \(h_p(z,w)\) of \({\mathcal H}_p\) is explicitly constructed. Also, a complete system of orthogonal functions of \({\mathcal H}_p\) are constructed using \(h_p(z,w)\) (\(p=1,2,\ldots\)).
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
- Shantou University China (People's Republic of)
- Academia Sinica Taiwan
complex projective space, Spectral problems; spectral geometry; scattering theory on manifolds, reproducing kernel, orthogonal system
complex projective space, Spectral problems; spectral geometry; scattering theory on manifolds, reproducing kernel, orthogonal system
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