The plaey-wiener-levinson theorem and the computation of strum-liouville eigenvalues: irregular sampling

References

• Algazin , S.D. 1995 . Calculating the Eigenvalues of Ordinary Differential Equations . Comp.Maths Math.Phys , 35 ( 4 ) : 477 – 482 .
   Web of Science ®Google Scholar
• Bailey , P.B. , Everitt , W.N. and Zettl , A. 1991 . Computing Eigenvalues of Singular Sturm-Liouville problems . Results in Mathematics , 20
   Google Scholar
• Bailey , P.B. , Everitt , W.N. and Zettl , A. 1996 . Regular and Singular Sturm-Liouville Problems with Coupled Boundary Conditions . Proc. Royal Soc. , 126 : 505 – 514 . (A)
   Google Scholar
• Bailey , P.B. , Gordon , M.K. and Shampine , L.F. 1978 . Automatic Solutzon of the Stun-Lzouuille Problem . ACM Trans. Math. Software , 4 : 193 – 208 . (A)
   Google Scholar
• Boumenir , A. and Chaname , B. 1996 . Eigenvalues of S-L Systems Using Sampling Theory . Applicable Analysis , 62 : 323 – 334 .
   Google Scholar
• Chanane , B. 1999 . Computing Eigenvalues of Regular Sturm-Liouville Problems . Applied Math.Letters , 12 : 119 – 125 .
   Google Scholar
• Chanane , B. 1998 . High Order Approximations of the Eigenvalues of Regular Sturm-Liouville Problems . J.Math.Anal.and Appl , 226 : 121 – 129 .
   Google Scholar
• Chanane , B. 1998 . Eigenvalues of Sturm-Liouville Problems Using Fliess Series . Applicable Analysis , 63 ( 3–4 ) : 233 – 238 .
   Google Scholar
• Chanane , B. 1998 . Eigenvalues of fourth order Sturm-Liouville Problems Using Fliess Series . J.Computational and Applied Math , 96 : 91 – 97 .
   Google Scholar
• Chanane , B. High Order Approximation of the Eigenvalues of Sturm-Liouville Problems with Coupled Self-Adjoint Boundary Conditions , Submitted .
   Google Scholar
• Chen , Xi . 1996 . The Shooting Method for Solving Eigenvalue Problems . J.Math. Anal and Appl , 203 : 435 – 450 .
   Google Scholar
• Everitt , W.N. and Nasri-Roudsari , G. 1996 . Interpolation and sampling theories, and linear ordinary boundary value problems . Univ.of Birmingham,School of Math,Pre-Print ,
   Google Scholar
• Fulton , C.T. and Pruess , S.A. 1993 . Mathematical Software for Sturm-Liouville Problems . ACM Trans.Math. Software , 19 : 360 – 376 .
   Google Scholar
• Fulton , C.T. and Pruess , S.A. 1994 . Eigenvalue and Eigenfunctions Asymptotics for Regular Sturm-Liouville Problems . J.Math.Anal.Appl , 188 : 297 – 340 .
   Google Scholar
• Garcia , A.G. 1997 . The Paley-Wiener-Levinson theorem revisied . Int.J.Math &Math.Sci , 20 ( 2 ) : 229 – 234 .
   Google Scholar
• Hargrave , B.A. 1976 . Numerical Approximation of Eigenvalues of Sturm-Liouville System . J.Computational Phys , 20 : 381 – 396 .
   Google Scholar
• Harris , B.J. 1994 . Asymptotics of Eigenvalues for Regular Sturn-Liouville Probelms . J.Math.Anal and Appl , 183 : 25 – 36 .
   Google Scholar
• Kong , Q. and Zettl , A. 1996 . Eigenvalue of Regular Sturm-Liouville Problems . J.Diff.Eqs , 131 : 1 – 19 .
   Google Scholar
• Marletta , M. and Pryce , J.D. 1992 . Automatic soultion of Sturm-Liouville problems using the Pruess method . J.Computational and Applied Mathematics , 39 : 57 – 78 .
   Google Scholar
• Naimark , M.A. 1968 . Linear Differential Operators . part II
   Google Scholar
• Paley , R. and Wiener , N. 1934 . “ Fourier Transform in the complex domains ” . In Amer.Math.Soc. Providence. R.I , Vol. 19 , AMS Colloquium Publ. Series .
   Google Scholar
• Pryce , J.D. 1993 . “ Numerical Solution of Sturm-Liouville Problems ” . Oxford Science Publications, Clarendon Press .
   Google Scholar
• Zayed , A.I. 1993 . A new role of Green's function in interpolation and sampling theory . J.Math.Anal and Appl , 175 : 222 – 238 .
   Web of Science ®Google Scholar
• Zayed , A.I. 1993 . Zayed, Advances in Shannon's Sampling Theory , CRC Press .
   Google Scholar