Sampling with a string
Abbreviated Journal Title
J. Fourier Anal. Appl.
Whittaker-Shannon's sampling theorem; Kramer's sampling theorem; Lagrange interpolation; string theory; Sturm-Liouville theory; STURM-LIOUVILLE PROBLEMS; LAGRANGE INTERPOLATION; COMPUTING EIGENVALUES; THEOREM; Mathematics, Applied
Kramer's sampling theorem forms a bridge between the Whittaker-ShannonKotel'nikov sampling theorem and boundary-value problems. It has been shown that sampling expansions associated with Sturm-Liouville boundary-value problems are Lagrange-type sampling series, i.e., Lagrange series with infinitely many terms converging to entire functions. String theory as developed by Feller, Kac, and Krein, is a generalization of the Sturm-Liouville theory. We investigate sampling series associated with strings and compare them with those associated with Sturm-Liouville problems. We show that unlike sampling series associated with Sturm-Liouville problems, those associated with strings include not only Lagrange-type sampling series, but also Lagrange polynomial interpolation.
Journal of Fourier Analysis and Applications
"Sampling with a string" (2002). Faculty Bibliography 2000s. 3092.