Jeffrey C. Lagarias: Papers on wavelets, tilings and fractals
The scaling functions associated to orthonormal wavelet bases
satisfy a functional equation (dilation equation) and give a
lattice tiling of R^n by translates of the function; see also the
list of papers on tilings.
- Two-scale difference equations I. Global regularity of
solutions ,
Ingrid Daubechies and Jeffrey C. Lagarias,
SIAM J. Math. Anal. 22 (1991), pp. 1388-1410.
- Two-scale difference equations II. Local regularity of
solutions and fractals ,
Ingrid Daubechies and Jeffrey C. Lagarias,
SIAM J. Math. Anal. 23 (1992), pp. 1031-1079.
- Sets of matrices all infinite products of which converge ,
Ingrid Daubechies and Jeffrey C. Lagarias,
Lin. Alg. Appl. 161 (1992), pp. 227-263.
- On the thermodynamic formalism for multifractal functions ,
Ingrid Daubechies and Jeffrey C. Lagarias,
Rev. Math. Physics 6 (1994), pp. 1033-1070.
[Also in: , The State of Matter, A volume dedicated to E. H. Lieb ,
(M. Aizenmann and H. Araki, Eds.), World Scientific: Singapore 1994,
pp. 213-264.]
- Haar-type Orthonormal Wavelet Bases in R^2 ,
Jeffrey C. Lagarias and Yang Wang,
J. Fourier Anal. Appl. 2 (1995) 1-14.
- Haar Bases for L^2(R^n) and Algebraic Number Theory,
Jeffrey C. Lagarias and Yang Wang,
J. Number Theory 57 (1996), pp. 181-197.
- The Finiteness Conjecture for the Generalized Spectral Radius of
a Set of Matrices ,
Jeffrey C. Lagarias and Yang Wang,
Lin. Alg. Appl. 214 (1995), pp. 17-42.
- Non-negative Radix Expansions for the Orthant ,
Jeffrey C. Lagarias and Yang Wang,
Trans. Amer. Math. Soc. 348 (1996), pp. 99-117.
- Self-Affine Tiles in R^n ,
Jeffrey C. Lagarias and Yang Wang,
Advances in Math. 121 (1996), pp. 21-49.
- Integral Self-Affine Tiles in R^n I. Standard and Nonstandard
Digit Sets ,
Jeffrey C. Lagarias and Yang Wang,
J. London Math. Soc. 54 (1996), pp. 161-179.
- Integral Self-Affine Tiles in R^n II. Lattice Tilings ,
Jeffrey C. Lagarias and Yang Wang,
J. Fourier Anal. Appl. 3 (1997), pp. 83-102.
- Spectral Sets and Factorizations of Finite Abelian Groups ,
Jeffrey C. Lagarias and Yang Wang,
J. Functional Analysis, 143 (1997), pp. 73-98.
[PostScript]
[Latex]
- Orthogonality Criteria for Compactly Supported Refinable Functions
and Function Vectors,
Jeffrey C. Lagarias and Yang Wang,
J. Fourier. Anal. Appl. ,
6 (2000), 153--170 .
[PostScript]
- Orthogonal bases of exponentials for the n-cube ,
Jeffrey C. Lagarias, James A. Reeds and Yang Wang,
Duke Math. J. ,
103 (2000), 25--37 .
[PostScript]
-
Universal spectra and Tijdeman's conjecture on factorization
of cyclic groups ,
J. C. Lagarias and Sandor Szabo,
J. Fourier Anal. Appl.,
7 (2001), 63--70 .
[PostScript]
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