Abstract Frame Theory

Title/Citation
Group-theoretic constructions of erasure-robust frames

M. Fickus, J. Jasper. D. Mixon, J. Peterson, Group-theoretic constructions of erasure-robust frames, submitted.

Spanning and independence properties of finite frames

P. C. Casazza, D. Speegle, Spanning and independence properties of finite frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

The simplified version of the Spielman-Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertibility theorem

P. G. Casazza, The simplified version of the Spielman-Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertibility theorem, unpublished notes.

The Kadison-Singer and Paulsen problems in finite frame theory

P. C. Casazza, The Kadison-Singer and Paulsen problems in finite frame theory, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

Algebraic geometry and finite frames

J. Cahill, N. Strawn, Algebraic geometry and finite frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

An elementary representation of all real Hessenberg unitary matrices

J. C. Tremain, C. Vaidyanathan, An elementary representation of all real Hessenberg unitary matrices, preprint (2012).

Necessary and sufficient conditions to perform spectral tetris

P. C. Casazza, A. Heinecke, K. Kornelson, Y. Wang, Z. Zhou, Necessary and sufficient conditions to perform spectral tetris, preprint (2012).

An elementary, illustrative proof of the Rado-Horn theorem

P. C. Casazza, J. Peterson, An elementary, illustrative proof of the Rado-Horn theorem, preprint (2012).

Operators and frames

J. Cahill, P. C. Casazza, G. Kutyniok, Operators and frames, preprint (2012).

Auto-tuning unit norm frames

P. G. Casazza, M. Fickus and D. G. Mixon, Auto-tuning unit norm frames, Appl. Comput. Harmon. Anal. 32 (2012), p 1-15.

Spanning and independence properties of frame partitions

B. G. Bodmann, P. G. Casazza, V. I. Paulsen and D. Speegle, Spanning and independence properties of frame partitions, Proceedings of AMS 140, No. 7 (2012), p. 2193 - 2207

Full spark frames

B. Alexeev, J. Cahill, D. G. Mixon, Full spark frames, preprint (2011).

Every Hilbert space frame has a Naimark complement

P. G. Casazza, M. Fickus, D. Mixon, J. Peterson and I. Smalyanau, Every Hilbert space frame has a Naimark complement, preprint (2011).

Algorithmic constructions of unitary matrices and tight frames

J. C. Tremain, Algorithmic constructions of unitary matrices and tight frames, preprint (2011).

The Paulsen problem in operator theory

J. Cahill and P. G. Casazza, The Paulsen problem in operator theory, submitted to Operators and Matrices (2011).

Constructing finite frames of a given spectrum and set of lengths

J. Cahill, M. Fickus, D. G. Mixon, M. J. Poteet and N. K. Strawn, Constructing finite frames of a given spectrum and set of lengths, submitted (2011).

A Quantitative Notion of Redundancy for Finite Frames

B. G. Bodmann, P. G. Casazza and G. Kutyniok, A Quantitative Notion of Redundancy for Finite Frames, Appl. and Comput. Harmonic Anal. 30 (2011) 348-362.

Optimally Sparse Frames

P. GP. G. Casazza, A. Heinecke, F. Krahmer and G. Kutyniok, Optimally Sparse Frames, IEEE Trans. Inform.Theory 57 (2011), 7279-7287.. Casazza, A. Heinecke, F. Krahmer and G. Kutyniok, Optimally Sparse Frames, IEEE Trans. Inform.Theory 57 (2011), 7279-7287.

A notion of redundancy for infinite frames

J. Cahill, P. G. Casazza and A. Heinecke, A notion of redundancy for infinite frames, Proceedings of SampTA 2011, Singapore. 

A quantitive notion of redundancy and its applications

B. G. Bodmann, P. G. Casazza and G. Kutyniok, A quantitive notion of redundancy and its applications, Proceedings of SampTA 2011, Singapore. 

Existence and Construction of Finite Frames with a Given Frame Operator

P.G. Casazza and M. Leon, Existence and Construction of Finite Frames with a Given Frame Operator, International Journal of Pure and Applied Mathematics, Vol. 63, No. 2 (2010), p. 149 - 158.

The road to equal-norm Parseval frames

B. G. Bodmann and P. G. Casazza, The road to equal-norm Parseval frames. Journal of Functional Analysis, Vol. 258 (2010) p. 397-420.

Upper and Lower Redundancy of Finite Frames

B. G. Bodmann, P. G. Casazza and G. Kutyniok, Upper and Lower Redundancy of Finite Frames. 43nd Annual Conference on Information Sciences and Systems (CISS) (Princeton University, NJ, 2010). 

When are frames close to equal-norm Parseval frames?

B. Bodmann and P.G. Casazza, When are frames close to equal-norm Parseval frames?, preprint (2009). 

Sums of Hilbert Space Frames

P.G. Casazza, S. Obeidat, S. Samarah and J.C. Tremain, Sums of Hilbert Space Frames, J. Math. Analysis and Appl. Vol. 351, Issue 2 (2009), 579-585. 

Sums of Hilbert Space Frames

P.G. Casazza, S. Obeidat, S. Samarah and J.C. Tremain, Sums of Hilbert Space Frames, J. Math. Analysis and Appl. Vol. 351, Issue 2 (2009), 579-585

Gradient descent of the frame potential

P.G. Casazza and M. Fickus, Gradient descent of the frame potential, Proc. Sampl. Theory Appl. (2009). 

Classes of Finite Equal Norm Parseval Frames

P.G. Casazza and N. Leonhard, Classes of Finite Equal Norm Parseval Frames, Contemp. Math. 451 (2008) 11-31. 

A New Frame Identity for Parseval Frames

R. Balan, P.G. Casazza, D. Edidin and G. Kutyniok, A New Frame Identity for Parseval Frames, Proceedings AMS, 135 No. 4 (2007) 1007-1015. 

A Generalization of Gram Schmidt Orthogonalization Generating all Parseval Frames

P.G. Casazza and G. Kutyniok, A Generalization of Gram Schmidt Orthogonalization Generating all Parseval Frames, Advances in Computational Mathematics, 18 (2007) 65-78. 

A Redundant Version of the Rado-Horn Theorem

P.G. Casazza, G. Kutyniok and D. Speegle, A Redundant Version of the Rado-Horn Theorem, Linear Algebra and Applications, 418 (2006) 1-10. 

Density, Overcompleteness and Localizations of Frames, I. Theory

R. Balan, P.G. Casazza, C. Heil and Z. Landau, Density, Overcompleteness and Localizations of Frames, I. Theory, Journal of Fourier Analysis and Applications, Vol. 12 No. 2 (2006) 105-143. 

Density Results for Frames of Exponentials

P.G. Casazza, O. Christensen, S. Li, and A. Lindner, Density Results for Frames of Exponentials, in Harmonic Analysis and Applications-in Honor of John Benedetto, C. Heil Ed., Birkhauser, (2006) 359-370. 

Density, Overcompleteness, and Localization of Frames

R. Balan, P.G. Casazza, C. Heil and Z. Landau, Density, Overcompleteness, and Localization of Frames, AMS Electronic Research Announcements, Vol. 12 (2006) 71-86. 

Existence and Construction of Finite Tight Frames

P.G. Casazza and M. Leon, Existence and Construction of Finite Tight Frames, Journal of Computational and Applied Mathematics, Vol. 4 No. 3 (2006) 277-289. 

A Physical Interpretation for Finite Tight Frames

P.G. Casazza, M. Fickus, J. Kovacevic, M. Leon and J.C. Tremain, A Physical Interpretation for Finite Tight Frames, in Harmonic Analysis and Applications (In Honor of John Benedetto), C. Heil, Ed. Birkhauser (2006) 51-78. 

The Known Equal Norm Parseval Frames as of 2005

P.G. Casazza and N. Leonhard, The Known Equal Norm Parseval Frames as of 2005, Preprint. 

Excess of Parseval Frames

R. Balan, P.G. Casazza, C. Heil and Z. Landau, Excess of Parseval Frames, Proceedings of SPIE, Vol. 5914 (2005) 591406 (1-7).

Decompositions of Frames and a new Frame Identity

R. Balan, P.G. Casazza, D. Edidin and G. Kutyniok, Decompositions of Frames and a new Frame Identity, Proceedings of SPIE, Vol. 5914 (2005) 591417 (1-10).

Projections of Frames

P.G. Casazza and M. Leon, Projections of Frames, Proceedings of SPIE, Vol. 5914 (2005) pp. 591402 (1-8). 

Duality Principles in Frame Theory

P.G. Casazza, G. Kutyniok and M.C. Lammers, Duality Principles in Frame Theory, Journal of Fourier Analysis and Applications, Vol. 10 (2004) pp. 383-408. 

Custom Building Finite Frames

P.G. Casazza, Custom Building Finite Frames, Contemporary Math. Vol. 345 (2004) pp. 61-86. 

Physical Laws Governing Finite Tight Frames

P.G. Casazza, M.C. Fickus, J. Kovacevic, M.T. Leon and J.C. Tremain, Physical Laws Governing Finite Tight Frames, Proceedings of SPIE, wavelets: Applications in signal and image processing X, M.A. Unser, A. Aldroubi, and A.F. Laine, editors. San Diego, 2003. Vol. 5207 pp. 371-380. 

Deficits and Excesses of Frames

R. Balan, P.G. Casazza, C. Heil and Z. Landau, Deficits and Excesses of Frames, Advances in Computational Mathematics Vol. 18, Nos. 2-4 (2003) pp.93-116. 

Uniform Tight Frames with Erasures

P.G. Casazza and J. Kovacevic, Uniform Tight Frames with Erasures, Advances in Computational Mathematics Vol. 18, Nos. 2-4 (2003) pp. 387-430. 

Riesz-Fischer Sequences and Lower Frame Bounds

P.G. Casazza, O. Christensen, S. Li, and A. Linder, Riesz-Fischer Sequences and Lower Frame Bounds, Journal for Analysis and its Applications, vol 21 No.2 (2002) 305-314. 

Frames of Translates

P.G. Casazza, O. Christensen, and N.J. Kalton, Frames of Translates, Collect. Math. 52,1 (2001) 35-54. 

Approximation of the Frame Coefficients using Finite-Dimensional Methods

P.G. Casazza and O. Christensen, Approximation of the Frame Coefficients using Finite-Dimensional Methods, Journal of Approximation Theory, 103 (2000) 338-356.

The Art of Frame Theory

P.G. Casazza, The Art of Frame Theory, Taiwanese Journal of Math., Vol 4 (2) (2000) 129-202. 

Every Frame is a Sum of Three (but not two) Orthonormal Bases and Other Frame Representations

P.G. Casazza, Every Frame is a Sum of Three (but not two) Orthonormal Bases and Other Frame Representations, Journal of Fourier Analysis and Applications, vol. 4 no. 6 (1998) p.727-732. 

Frames Containing a Riesz Basis and Preservation of this Property under Pertubations

P.G. Casazza and O. Christensen, Frames Containing a Riesz Basis and Preservation of this Property under Pertubations, SIAM Journal on Math Analysis, Vol. 29, No. 1 (1998) p. 266-278.

Riesz Frames and Finite Dimensional Approaches to Problems in Frame Theory

P.G. Casazza and O. Christensen, Riesz Frames and Finite Dimensional Approaches to Problems in Frame Theory, Journal of Approximation Theory and its Applications 101 (1998). 

Approximation of the Frame Coefficients using Finite-Dimensional Methods

P.G. Casazza and O. Christensen, Approximation of the Frame Coefficients using Finite-Dimensional Methods, Journal of Electronic Imaging, special Volume 1997, "Best Papers in Electronic Imaging", Vol. 6, No. 4 (1997) p. 479-483. 

Characterizing Hilbert Space Frames with the Subframe Property

P.G. Casazza, Characterizing Hilbert Space Frames with the Subframe Property, Illinois Journal of Mathematics, Vol. 41, No. 4 (1997) p.648-666. 

Pertubation of Operators and Applications to Frame Theory

P.G. Casazza and Ole Christensen, Pertubation of Operators and Applications to Frame Theory, Journal of Fourier Analysis and Applications, Vol. 3, No. 5 (1997) p. 543-557.

Path Connectedness of the Wavelet Transform

P.G. Casazza and M.T. Leon, Path Connectedness of the Wavelet Transform, (Submitted, 10 pages).