School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160
(404) 894-9231
h e i l @ m a t h . g a t e c h . e d u
Vita
Complete Publication List
Publication List with Abstracts
Links to many individual papers are provided below.
Please email me to request a copy of any paper that is not available
electronically.
Books and Manuscripts
- C. Heil,
Introduction to Harmonic Analysis, in preparation.
Current table of contents (as of September 2009).
- C. Heil,
A Basis Theory Primer, in preparation.
Current table of contents (as of September 2009).
- C. Heil, editor,
Harmonic Analysis and Applications,
A volume in honor of John J. Benedetto,
Birkhäuser, Boston, 2006.
Table of Contents.
Foreword by
Hans Feichtinger.
Preface.
- C. Heil and D. F. Walnut, editors,
Fundamental Papers in Wavelet Theory, Princeton University Press,
Princeton, NJ, 2006.
Table of Contents.
Foreword by
Ingrid Daubechies.
- C. Heil, P. E. T. Jorgensen, and D. R. Larson, editors,
Wavelets, Frames, and Operator Theory
(Baltimore, 2003), Contemporary Math., Vol. 345,
Amer. Math. Soc., Providence, RI, 2004.
- C. Heil,
A Basis Theory Primer, 1997 (unpublished manuscript, 93 pages).
Surveys and Pretty Good Expository Papers
- C. Heil,
The Density Theorem and the Homogeneous Approximation Property
for Gabor frames, in: "Representations, Wavelets, and Frames:
A Celebration of the Mathematical Work of Lawrence Baggett,"
P. E. T. Jorgensen, K. D. Merrill, and J. A. Packer, eds.,
Birkhäuser, Boston (2008), 71-102.
- C. Heil and D. R. Larson,
Operator theory and modulation spaces,
in: "Frames and Operator Theory in Analysis and Signal Processing"
(San Antonio, 2006),
Comtemp. Math., Vol. 451, Amer. Math. Soc., Providence, RI (2008), 137-150.
- C. Heil,
History and evolution of the Density Theorem for Gabor frames,
J. Fourier Anal. Appl., 13 (2007), 113-166.
- C. Heil,
Linear independence of finite Gabor systems,
in: "Harmonic Analysis and Applications,"
Birkhäuser, Boston (2006), 171-206.
Errata.
- C. Heil,
Integral operators, pseudodifferential operators, and Gabor frames,
in: "Advances
in Gabor Analysis," H. G. Feichtinger and T. Strohmer, eds.,
Birkhäuser, Boston (2003), 153-169.
- C. Heil,
An introduction to weighted Wiener amalgams,
in: "Wavelets and their Applications" (Chennai, January 2002),
M. Krishna, R. Radha and S. Thangavelu, eds.,
Allied Publishers, New Delhi (2003), 183-216.
- J. J. Benedetto, C. Heil, and D. F. Walnut,
Differentiation and the Balian-Low theorem,
J. Fourier Anal. Appl., 1 (1995), 355-402.
- C. Heil and G. Strang,
Continuity of the joint spectral radius: Application to wavelets,
in: "Linear Algebra for Signal Processing" (Minneapolis, MN, 1992),
A. Bojanczyk and G. Cybenko, eds., IMA Vol. Math. Appl. 69,
Springer-Verlag, New York (1995), 51-61.
- D. Colella and C. Heil,
Dilation equations and the smoothness of compactly supported wavelets,
in: "Wavelets: Mathematics and Applications,"
J. J. Benedetto and M. W. Frazier, eds.,
CRC Press, Boca Raton, FL (1994), 163-201.
- C. Heil,
Methods of solving dilation equations,
in: "Probabilistic and Stochastic Methods in Analysis, with Applications"
(Il Ciocco, 1991), J. S. Byrnes et al., eds., NATO Adv. Sci. Inst. Ser. C:
Math. Phys. Sci. 372, Kluwer, Dordrecht (1992), 15-45.
- C. E. Heil and D. F. Walnut,
Continuous and discrete wavelet transforms,
SIAM Review, 31 (1989), 628-666.
Localized Frames, Density, Excess, and the HAP
- C. Heil and G. Kutyniok,
Density of frames and Schauder bases of windowed exponentials,
Houston J. Math., 34 (2008), 565-600.
- C. Heil,
The Density Theorem and the Homogeneous Approximation Property
for Gabor frames, in: "Representations, Wavelets, and Frames:
A Celebration of the Mathematical Work of Lawrence Baggett,"
P. E. T. Jorgensen, K. D. Merrill, and J. A. Packer, eds.,
Birkhäuser, Boston (2008), 71-102.
- C. Heil and G. Kutyniok,
The Homogeneous Approximation Property for wavelet frames,
J. Approx. Theory, 147 (2007), 28-46.
- C. Heil,
History and evolution of the Density Theorem for Gabor frames,
J. Fourier Anal. Appl., 13 (2007), 113-166.
- R. Balan, P. G. Casazza, C. Heil, and Z. Landau,
Density, overcompleteness, and localization of frames,
Electron. Res. Announc. Amer. Math. Soc., 12 (2006), 71-86.
- R. Balan, P. G. Casazza, C. Heil, and Z. Landau,
Density, overcompleteness, and localization of frames, II. Gabor systems,
J. Fourier Anal. Appl., 12 (2006), 307-344.
Errata.
- R. Balan, P. G. Casazza, C. Heil, and Z. Landau,
Density, overcompleteness, and localization of frames, I. Theory,
J. Fourier Anal. Appl., 12 (2006), 105-143.
Transparencies from a related
talk given at the
2nd International Conference on Computational Harmonic Analysis,
Vanderbilt University, May 27, 2004, and another
talk given at the University of Maryland, March 14, 2005.
- C. Heil and G. Kutyniok,
Density of weighted wavelet frames,
J. Geometric Analysis, 13 (2003), pp. 479-493.
- R. Balan, P. G. Casazza, C. Heil, and Z. Landau,
Excesses of Gabor frames,
Appl. Comput. Harmon. Anal., 14 (2003), 87-106.
- R. Balan, P. G. Casazza, C. Heil, and Z. Landau,
Deficits and excesses of frames,
Adv. Comput. Math.,
Special Issue on Frames, 18 (2003), 93-116.
- B. Deng and C. Heil,
Density of Gabor Schauder bases,
in: "Wavelet Applications in Signal and Image Processing VIII,"
(San Diego, CA, 2000), Proc. SPIE Vol. 4119, A. Aldroubi et al., eds.,
SPIE, Bellingham, WA (2000), 153-164.
- O. Christensen, B. Deng, and C. Heil,
Density of Gabor frames,
Appl. Comput. Harmon. Anal., 7 (1999), 292-304.
Errata.
Pseudodifferential Operators
- Á. Bényi, K. Gröchenig, C. Heil, and K. Okoudjou,
Modulation spaces and a class of bounded multilinear pseudodifferential
operators, J. Operator Theory, 54 (2005), 387-399.
- K. Gröchenig and C. Heil,
Counterexamples for boundedness of pseudodifferential operators,
Osaka J. Math., 41 (2004), 681-691.
- C. Heil,
Integral operators, pseudodifferential operators, and Gabor frames,
in: "Advances
in Gabor Analysis," H. G. Feichtinger and T. Strohmer, eds.,
Birkhäuser, Boston (2003), 153-169.
- K. Gröchenig and C. Heil,
Modulation spaces as symbol classes for pseudodifferential operators,
in: "Wavelets and their Applications" (Chennai, January 2002),
M. Krishna, R. Radha and S. Thangavelu, eds.,
Allied Publishers, New Delhi (2003), 151-169.
- K. Gröchenig and C. Heil,
Modulation spaces and pseudodifferential operators,
Integral Equations Operator Theory, 34 (1999), 439-457.
- C. Heil, J. Ramanathan, and P. Topiwala,
Singular values of compact pseudodifferential operators,
J. Funct. Anal., 150 (1997), 426-452.
Errata.
Time-Frequency Analysis and Gabor Systems
- C. Heil and A. M. Powell,
Regularity for complete and minimal Gabor systems on a lattice,
submitted.
- C. Heil and D. R. Larson,
Operator theory and modulation spaces,
in: "Frames and Operator Theory in Analysis and Signal Processing"
(San Antonio, 2006),
Comtemp. Math., Vol. 451, Amer. Math. Soc., Providence, RI (2008), 137-150.
- C. Heil and A. M. Powell,
Gabor Schauder Bases and the Balian-Low Theorem,
J. Math. Physics, 47 (2006).
- C. Heil,
Linear independence of finite Gabor systems,
in: "Harmonic Analysis and Applications,"
Birkhäuser, Boston (2006), 171-206.
Errata.
- K. Gröchenig, C. Heil, and K. Okoudjou,
Gabor analysis in weighted amalgam spaces,
Sampling Theory in Signal and Image Processing, 1 (2003), 225-259.
- K. Gröchenig, D. Han, C. Heil, G. Kutyniok,
The Balian-Low theorem for symplectic lattices in higher dimensions,
Appl. Comput. Harmon. Anal., 13 (2002), 169-176.
- K. Gröchenig and C. Heil,
Gabor meets Littlewood-Paley: Gabor expansions in L^p(R^d),
Studia Math., 146 (2001), 15-33.
- J. J. Benedetto, C. Heil, and D. F. Walnut,
Gabor systems and the Balian-Low theorem, in:
"Gabor Analysis and Algorithms: Theory and Applications,"
H. G. Feichtinger and T. Strohmer, eds., Birkhäuser, Boston (1998), 85-122.
- C. Heil, J. Ramanathan, and P. Topiwala,
Linear independence of time-frequency translates,
Proc. Amer. Math. Soc., 124 (1996), 2787-2795.
- J. J. Benedetto, C. Heil, and D. F. Walnut,
Differentiation and the Balian-Low theorem,
J. Fourier Anal. Appl., 1 (1995), 355-402.
- J. Benedetto, C. Heil, and D. Walnut,
Uncertainty Principles for time-frequency operators,
in: "Continuous and Discrete Fourier Transforms, Extension Problems and
Wiener-Hopf Equations," Oper. Theory Adv. Appl. 58,
I. Gohberg, ed., Birkhäuser, Basel (1992), 1-25.
- C. Heil and D. Walnut,
Gabor and wavelet expansions,
in: "Recent Advances in Fourier Analysis and its Applications"
(Il Ciocco, 1989), J. S. Byrnes and J. L. Byrnes, eds., NATO Adv. Sci. Inst.
Ser. C: Math. Phys. Sci. 315, Kluwer, Dordrecht (1990), 441-454.
- C. Heil,
A discrete Zak transform,
Technical Report, The MITRE Corporation, December 1989.
- C. E. Heil and D. F. Walnut,
Continuous and discrete wavelet transforms,
SIAM Review, 31 (1989), 628-666.
Frame Theory, Sampling, and Shift-Invariant Spaces
- A. Aldroubi, C. Cabrelli, C. Heil, K. Kornelson, and U. Molter,
Invariance of a shift-invariant space,
J. Fourier Anal. Appl., to appear.
- S. Bishop, C. Heil, Y. Y. Koo, and J. K. Lim,
Invariances of frame sequences under perturbation,
submitted.
- C. Heil, Y. Y. Koo, and J. K. Lim,
Duals of frame sequences, Acta Appl. Math., 107 (2009), 75-90.
The
published version is available at www.springerlink.com.
- K. Gröchenig, C. Heil, and D. Walnut,
Nonperiodic sampling and the local three squares theorem,
Ark. Mat., 38 (2000), 77-92.
- O. Christensen and C. Heil,
Perturbations of Banach frames and atomic decompositions,
Math. Nachr., 186 (1997), 33-47.
- C. E. Heil and D. F. Walnut,
Continuous and discrete wavelet transforms,
SIAM Review, 31 (1989), 628-666.
Wavelets, Refinable Functions, and the Joint Spectral Radius
- C. A. Cabrelli, C. Heil, and U. M. Molter,
Self-similarity and multiwavelets in higher dimensions,
Memoirs Amer. Math. Soc., Vol. 170, No. 807 (2004), 82 pages.
- C. A. Cabrelli, C. Heil, and U. M. Molter,
Multiwavelets in R^n with an arbitrary dilation matrix,
in: "Wavelets and Signal Processing," L. Debnath, ed.,
Birkhäuser, Boston (2003), 23-39.
- C. Cabrelli, C. Heil, and U. Molter,
Accuracy of several multi-dimensional refinable distributions,
J. Fourier Anal. Appl., 6 (2000), 483-502.
- C. A. Cabrelli, C. Heil, and U. M. Molter,
Necessary conditions for the existence of multivariate multiscaling
functions, in: "Wavelet Applications in Signal and Image Processing VIII"
(San Diego, CA, 2000), Proc. SPIE Vol. 4119, A. Aldroubi et al., eds.,
SPIE, Bellingham, WA (2000), 395-406.
- C. A. Cabrelli, C. Heil, and U. M. Molter,
Polynomial reproduction by refinable functions,
in: "Advances in Wavelets" (Hong Kong, 1997),
K.-S. Lau, ed., Springer-Verlag, Singapore (1999), 121-161.
- C. Cabrelli, C. Heil, and U. Molter,
Accuracy of lattice translates of several multidimensional refinable
functions, J. Approx. Theory, 95 (1998), 5-52.
Errata.
- C. Heil and D. Colella,
Matrix refinement equations: Existence and uniqueness,
J. Fourier Anal. Appl., 2 (1996), 363-377.
- C. Heil, G. Strang and V. Strela,
Approximation by translates of refinable functions,
Numerische Math., 73 (1996), 75-94.
Errata.
- C. Heil and G. Strang,
Continuity of the joint spectral radius: Application to wavelets,
in: "Linear Algebra for Signal Processing" (Minneapolis, MN, 1992),
A. Bojanczyk and G. Cybenko, eds., IMA Vol. Math. Appl. 69,
Springer-Verlag, New York (1995), 51-61.
- C. Heil and D. Colella,
Sobolev regularity for scaling functions via ergodic theory,
in: "Approximation Theory VIII," Vol. 2 (College Station, TX, 1995),
C. K. Chui and L. L. Schumaker, eds.,
World Scientific, Singapore (1995), 151-158.
- D. Colella and C. Heil,
Dilation equations and the smoothness of compactly supported wavelets,
in: "Wavelets: Mathematics and Applications,"
J. J. Benedetto and M. W. Frazier, eds.,
CRC Press, Boca Raton, FL (1994), 163-201.
- D. Colella and C. Heil,
Characterizations of scaling functions: Continuous solutions,
SIAM J. Matrix Anal. Appl., 15 (1994), 496-518.
- C. Heil,
Some stability properties of wavelets and scaling functions,
in: "Wavelets and Their Applications: (Il Ciocco, 1992),
J. S. Byrnes et al., eds., NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci.
442, Kluwer, Dordrecht (1994), 19-38.
- D. Colella and C. Heil,
The characterization of continuous, four-coefficient scaling functions
and wavelets, IEEE Trans. Inform. Theory, 38 (1992), 876-881.
- C. Heil,
Methods of solving dilation equations,
in: "Probabilistic and Stochastic Methods in Analysis, with Applications"
(Il Ciocco, 1991), J. S. Byrnes et al., eds., NATO Adv. Sci. Inst. Ser. C:
Math. Phys. Sci. 372, Kluwer, Dordrecht (1992), 15-45.
- C. E. Heil and D. F. Walnut,
Continuous and discrete wavelet transforms,
SIAM Review, 31 (1989), 628-666.
Image Processing
- R. Ashino, S. J. Desjardins, C. Heil, M. Nagase, and R. Vaillancourt,
Pseudodifferential operators, microlocal analysis and image restoration, in:
"Advances in Pseudo-Differential Operators,"
R. Ashino, P. Boggiatto, and M.-W. Wong, eds.,
Birkhäuser, Boston (2004), 187-202.
- R. Ashino, S. J. Desjardins, C. Heil, M. Nagase, and R. Vaillancourt,
Smooth tight frame wavelets and image analysis in Fourier space,
Comput. Math. Appl., 45 (2003), 1551-1579.
- R. Ashino, S. J. Desjardins, C. Heil, M. Nagase, and R. Vaillancourt,
Microlocal analysis, smooth frames and denoising in Fourier space,
Asian Information-Science-Life, 1 (2002), 153-160.
- R. Ashino, S. J. Desjardins, C. Heil, M. Nagase, and R. Vaillancourt,
Microlocal filtering with multiwavelets,
Comput. Math. Appl., 41 (2001), 111-133.
- V. Strela, P. N. Heller, G. Strang, P. Topiwala, and C. Heil,
The application of multiwavelet filterbanks to image processing,
IEEE Trans. Image Proc, 8 (1999), 548-563.
Generalized Harmonic Analysis
Conference Proceedings and Other
Publications
- S. Bishop, C. Heil, Y. Y. Koo, and J. K. Lim,
Duals and invariances of frame sequences,
in: "Wavelets~XIII" (San Diego, CA, 2009), Proc. SPIE Vol. 7446,
V. Goyal et al., eds., SPIE, Bellingham, WA (2009), 74460K1--74460K8.
- C. Heil and G. Kutyniok,
Convolution and Wiener amalgam spaces on the affine group,
in: "Recent Advances in Computational Science,"
P. E. T. Jorgensen, X. Shen, C.-W. Shu, and N. Yan, eds.,
World Scientific, Singapore (2008), 209-217.
- R. Balan, P. G. Casazza, C. Heil, and Z. Landau,
Excess of Parseval frames,
in: "Wavelets XI" (San Diego, CA, 2005), Proc. SPIE Vol. 5914,
M. Papadakis et al., eds., SPIE, Bellingham, WA (2005), 39-46.
- R. Ashino, S. J. Desjardins, C. Heil, M. Nagase, and R. Vaillancourt,
Image restoration through microlocal analysis with smooth tight
wavelet frames, in: "Theoretical development and feasibility of mathematical
analysis on the computer" (Kyoto, 2002), Surikaisekikenkyusho Kokyuroku
No. 1286 (2002), 101-118.
- R. Ashino, C. Heil, M. Nagase, and R. Vaillancourt,
Multiwavelets, pseudodifferential operators and microlocal analysis,
in: "Wavelet Analysis and Applications" (Guangzhou, China, 1999),
D. Deng et al., eds., AMS/IP Stud. Adv. Math., 25,
American Mathematical Society, Providence, RI (2002), 9-20.
- R. Ashino, C. Heil, M. Nagase, and R. Vaillancourt,
Microlocal analysis and multiwavelets, in:
"Geometry, Analysis and Applications" (Varanasi, India, 2000),
R. S. Pathak, ed., World Scientific, Singapore (2001), 293-302.
- C. Heil,
Wavelets, Section 7.13.6 in the CRC Standard Mathematical Tables and Formulae,
30th Edition, D. Zwillinger, ed., CRC Press, Boca Raton, FL (1996), 663-667
(Section 7.15.5 in the 31st Edition, 2003, 723-726).
- C. Heil,
Existence and accuracy for matrix refinement equations,
Z. Angew. Math. Mech., Special issue on Applied Stochastics and Optimization,
76 (1996), 251-254.
- P. N. Heller, V. Strela, G. Strang, P. Topiwala,
C. Heil, and L. S. Hills,
Multiwavelet filter banks for data compression,
in: ISCAS '95, Proc. International Symposium on Circuits and Systems
(Seattle, WA, 1995), Vol. 3, IEEE, Piscataway, NJ (1995), 1796-1799.
- C. Heil, J. Ramanathan, and P. Topiwala,
Asymptotic singular value decay of time-frequency localization operators,
in: "Wavelet Applications in Signal and Image Processing II"
(San Diego, CA, 1994), Proc. SPIE Vol. 2303, A. F. Laine and M. A. Unser, eds.,
SPIE, Bellingham, WA (1994), 15-24.
- C. Heil,
Applications of the fast wavelet transform,
in: "Advanced Signal-Processing Algorithms, Architectures, and Implementations"
(San Diego, CA, 1990), Proc. SPIE Vol. 1348, F. T. Luk, ed.,
SPIE, Bellingham, WA (1990), 248-259.
- C. Heil,
Wavelets and frames,
in: "Signal Processing, Part I: Signal Processing Theory,"
L. Auslander, T. Kailath, and S. Mitter, eds., IMA Vol. Math. Appl. 22,
Springer-Verlag, New York (1990), 147-160.
- C. E. Heil and D. F. Walnut,
Continuous and discrete wavelet transforms,
SIAM Review, 31 (1989), 628-666.
Book Reviews
-
Review of "Ten Lectures on Wavelets"
by I. Daubechies (review appeared in SIAM Review, 35 (1993), 666-669).
-
Review of "A First Course in Fourier Analysis,"
by D. W. Kammler (review appeared in SIAM Review, 43 (2001) 722-724).