Universal truncation error upper bounds in irregular sampling restoration^†

References

• Marvasti , F . 2001 . Nonuniform Sampling: Theory and Practice , Boston : Kluwer Academic Publishers .
   Google Scholar
• Hinsen , G . 1993 . Irregular sampling of bandlimited L p –functions . J. Approx. Theory , 72 : 346 – 364 .
   Web of Science ®Google Scholar
• Hinsen , G and Klösters , D . 1993 . The sampling series as a limiting case of Lagrange interpolation . Appl. Anal. , 49 : 49 – 60 .
   Google Scholar
• Aldroubi , A and Feichtinger , H . 1998 . Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The L p -theory . Proc. Amer. Math. Soc. , 126 ( 9 ) : 2677 – 2686 .
   Web of Science ®Google Scholar
• Feichtinger , H and Gröchenig , K . 1992 . Irregular sampling theorems and series expansions of band-limited functions . J. Math. Anal. Appl. , 167 : 530 – 556 .
   Web of Science ®Google Scholar
• Feichtinger , H and Gröchenig , K . 1992 . Iterative reconstruction of multivariate band-limited functions from irregular sampling values . SIAM J. Math. Anal. , 23 ( 1 ) : 244 – 261 .
   Web of Science ®Google Scholar
• Greengard , L , Lee , J-Y and Inati , S . 2006 . The fast sinc transform and image reconstruction from nonuniform samples in k-space . Commun. Appl. Math. and Comput. Sci. , 1 ( 1 ) : 121 – 131 .
   Google Scholar
• Higgins , JR , Schmeisser , G and Voss , JJ . 2000 . The sampling theorem and several equivalent results in analysis . J. Comput. Anal. Appl. , 2 : 333 – 371 .
   Google Scholar
• Flornes , KM , Lyubarskii , Yu and Seip , K . 2000 . A direct interpolation method for irregular sampling . Appl. Comput. Harmon. Anal. , 8 ( 1 ) : 113 – 121 .
   Google Scholar
• Olenko , AYa and Pogány , TK . 2003 . Direct Lagrange–Yen type interpolation of random fields . Theory Stoch. Process. , 9 (25) ( 3–4 ) : 242 – 254 .
   Google Scholar
• Olenko , AYa and Pogány , TK . 2004 . Sharp exact upper bound for interpolation remainder of random processes . Theory Probab. Math. Statist. , 71 : 133 – 144 .
   Google Scholar
• Olenko , AYa and Pogány , TK . 2007 . On sharp exact bounds for remainders in multidimensional sampling theorem . Sampl. Theory Signal Image Process. , 6 ( 3 ) : 249 – 272 .
   Google Scholar
• A.Ya. Olenko and T.K. Pogány Universal truncation error upper bounds in sampling restoration. Georgian Math. J. (in print).
   Google Scholar
• Yen , JL . 1956 . On nonuniform sampling of bandwidth limited signals . IRE Trans. Circuit Theory , CT-3 : 251 – 257 .
   Google Scholar
• Plancherel , M and Pólya , Gy . 1937 . Fonctions entières et intégrales de Fourier multiples II . Comment. Math. Helv. , 10 : 110 – 163 .
   Google Scholar
• R.P. Boas Jr, Entire Functions, Academic Press, New York, 1954.
   Google Scholar
• Plancherel , M and Pólya , Gy . 1937 . Fonctions entières et intégrales de Fourier multiples . Comment. Math. Helv. , 9 : 224 – 248 .
   Google Scholar
• Boas , RP Jr . 1940 . Entire functions bounded on a line . Duke Math. J. , 6 : 148 – 169 .
   Google Scholar
• Lindner , AM . 1999 . On lower bounds of exponential frames . J. Fourier Anal. Appl. , 5 ( 2 ) : 187 – 194 .
   Web of Science ®Google Scholar
• Nikolskii , SM . 1975 . Approximation of Functions of Several Variables and Imbedding Theorems , New York : Springer-Verlag .
   Google Scholar
• Pogány , TK . 2003 . Multidimensional Lagrange–Yen interpolation via Kotel'nikov–Shannon sampling formulas . Ukr. Math. J. , 50 ( 11 ) : 1810 – 1827 .
   Google Scholar
• Pogány , TK . 1996 . Statistical estimation of the bandwidth from irregularly spaced data . Signal Process. , 54 ( 1 ) : 75 – 80 .
   Web of Science ®Google Scholar
• Higgins , JR . 1996 . Sampling in Fourier and Signal Analysis: Foundations , Oxford : Clarendon Press .
   Google Scholar
• Seip , K . 2004 . Interpolation and Sampling in Spaces of Analytic Functions , Providence, RI : American Mathematical Society .
   Google Scholar
• Weisstein E.W. Lambert W-Function, MathWorld – A Wolfram Web Resource. Available at http://mathworld.wolfram.com/LambertW-Function.html.
   Google Scholar
• Li , XM . 1998 . Uniform bounds for sampling expansions . J. Approx. Theory , 93 ( 1 ) : 100 – 113 .
   Web of Science ®Google Scholar
• Long , J and Fang , G . 2003 . On uniform truncation error upper bounds and aliasing error for multidimensional sampling expansion . Sampl. Theory Signal Image Process. , 2 ( 2 ) : 103 – 115 .
   Google Scholar
• Olenko , AYa and Pogány , TK . 2006 . Time shifted aliasing error upper bounds for truncated sampling cardinal series . J. Math. Anal. Appl. , 324 : 262 – 280 .
   Web of Science ®Google Scholar
• Yaglom , AM . 1986 . “ Correlation Theory of Stationary and Related Random Functions II ” . In Supplementary Notes and References , New York, Berlin, Heidelberg, London, Paris, Tokyo : Springer-Verlag .
   Google Scholar