References
- Gundy , RF . 1966 . Martingale theory and pointwise convergence of certain orthogonal series . Trans. Amer. Math. Soc. , 124 : 228 – 248 .
- Denny , JL and Abbey , CK . 1998 . Partial sums of orthogonal bases preserving positivity–and martingales . J Fourier Anal. App. , 4 ( 2 ) : 151 – 157 .
- Wojtaszczyk , P . 1997 . A Mathematical Introduction to Wavelets, volume 37 of London Mathematical Society Student Texts , Cambridge : Cambridge University Press .
- Gröchenig , K and Madych , WR . 1992 . Multiresolution analysis, Haar bases, and self-similar tilings of ℛ n . IEEE Trans. Inform. Theory , 38 : 556 – 568 .
- Lagarias , JC and Wang , Y . 1995 . Haar type orthonormal wavelet bases in ℛ 2 . J. Fourier Anal. Appl. , 2 ( 1 ) : 1 – 14 .
- Lagarias , JC and Wang , Y . 1996 . Haar bases for and algebraic number theory . J. Number Theory , 57 ( 1 ) : 181 – 197 .
- Lagarias , JC and Wang , Y . 1999 . Corrigendum/addendum: Haar bases for and algebraic number theory . J. Number Theory , 76 ( 2 ) : 330 – 336 .
- Benassi , A , Jaffard , S and Roux , D . 1993 . Analyse multi-échelle des processus gaussiens markoviens d'ordre p indexés par (0, 1) . Stochastic Process. Appl. , 47 : 275 – 297 .
- G[ibar]hman , Ĭ[Ibar] and Skorohod , AV . The Theory of Stochastic Processes. I, volume 210 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] , Berlin : Springer-Verlag . English Edition, 1980. Translated from the Russian by Samuel Kotz
- Gundy , RF and Kazarian , K . 2000 . Stopping times and local convergence for spline wavelet expansions . SIAM J. Math. Anal. , 31 ( 3 ) : 561 – 573 . (electronic)
- Dudley , RM . 1989 . Real Analysis and Probability , The Wadsworth & Brooks/Cole Mathematics Series Pacific Grove, CA : Wadsworth & Brooks/Cole Advanced Books & Software .
- Doob , JL . 1990 . Stochastic Processes , New York : Wiley Classics Library. John Wiley & Sons Inc . Reprint of the 1953 original, A Wiley-Interscience Publication
- Olevskiĭ , AM . 1975 . Fourier Series with Respect to General Orthogonal Systems , New York : Springer-Verlag . Translated from the Russian by B. Marshall, P. Christoffers. H.J. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 86
- Lamb , CW . 1974 . Representation of functions as limits of martingales . Trans. Amer. Math. Soc. , 188 : 395 – 405 .
- Chow , YS . 1962/1963 . Convergence theorems of martingales . Z Wahrscheinlichkeitstheorie und Verw. Gebiete , 1 : 340 – 346 .
- Flaherty , T and Wang , Y . 1999 . Haar-type multiwavelet bases and self-affine multi-tiles . Asian J. Math. , 3 ( 2 ) : 387 – 400 .
- Gröchenig , K , Haas , A and Raugi , A . 1999 . Self-affine tilings with several tiles. I . Appl. Comput. Harmon. Anal. , 7 ( 2 ) : 211 – 238 .