David R. Larson

Research Interests

  • Functional Analysis
  • Operator Algebras and Operator Theory
  • Applied Harmonic Analysis
  • Frame Theory

    • Curriculum Vitae

    arXiv

    Research Articles:

  • R. Hotovy, D.R. Larson, S. Scholze, " Binary frames "to appear. arXiv
  • D. Han, D. Larson, B. Liu and R. Liu, " Operator-valued measures, dilations, and the theory of frames "to appear. arXiv
  • J. Fang, D. Larson and S. Rowe" ,P1-subalgebras of Mn(C) " , Involve, to appear.
  • S. Djordjevic, R. Harte and D. Larson, " Partially invariant subspaces," Operators and Matrices , to appear.
  • D. Dutkay, D.R. Larson and S. Silvestrov," Irreducible wavelet representations and ergodic automorphisms on solenoids, " Operators and Matrices, to appear. arXiv
  • J. Giol, L. Kovalev, D. Larson, N. Nguyen and J. Tener, " Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames" , Operators and Matrices, 5(2011), 139-155. arXiv
  • D. Han and D.R. Larson, "Unitary systems and Bessel generator multipliers, " Wavelets and Multiscale Analysis, Springer (2010), 129-148.

    • 2010

  • D. Dutkay, D. Han and D.R. Larson, "A duality principle for groups, " J. Funct. Anal. 257(2009), 1133-1143. arXiv
  • D. Han and D.R. Larson ", On the orthogonality of frames and the density and connectivity of wavelet frames" , Acta. Appl. Math. 107(2009), 211-222.
  • D. Larson, P. Massopust and G. Olafsson, "Three-way tiling sets in two dimensions", Acta. Appl. Math. 108(2009), 529-546. arXiv
  • V. Kaftal, D.R. Larson and S. Zhang, "Operator valued frames" Transactions AMS 361 (2009), 6349-6385.arXiv
  • D. Han and D.R. Larson, "Duality properties for projective unitary representations, "Bull. London Math. Soc. 40(2008), 685-695.
  • D. Han, D. Larson and J. Wu, "Riesz bases and their dual modular frames in Hilbert C*-algebras, "J. Math. Anal. Appl. 343(2008), 246-256.
  • V. Kaftal, D.R.Larson and S. Zhang, "Operator valued frames on C*-modules" Contemp. Math. 451(2008), 171-185. arXiv
  • A.J, Hergenroeder, Z. Catlin, B. George and D. Larson, "Patch and crossover planar dyadic wavelet sets", Involve vol. 1 (2008), 59-90.
  • X. Zhang and D.R. Larson, "Interpolation maps and congruence domains for wavelet sets" Representations, Wavlets and Frames, Birkhauser Verlag Basel (2008), 193-214. arXiv
  • D.R. Larson and P. Massopust, "Coxeter groups and wavelet sets," Contemp. Math. 451 (2008), 187-218. arXiv
  • C. Heil and D.R. Larson, "Operator theory and modulation spaces" Contemp. Math. 451 (2008), 137-150.
  • D.R. Larson, "Unitary systems, wavelet sets, and operator-theoretic interpolation of wavelets and frames," Institute for Math. Sci., National University of Singapore, World scientific (2007), 166-214.
  • D. Han, D.R. Larson, Z. Pan and W. Wogen, "Separating vectors for operators", Proc.AMS 135 (2007), 713-724.
  • D.R. Larson, W-S. Tang and E. Weber, "Robertson type theorems for countable abelian groups of unitary operators", Contemporary Math. 414 (2006), 289-295.
  • D.R. Larson, "Unitary systems and wavelet sets, " Wavelet Analysis and Applications, Applied and Numerical Harmonic Analysis, Birkhauser Verlan Basel (2006), 143-171.
  • D.R. Larson, E. Schulz, D. Speegle and K.F. Taylor, "Explicit cross sections of singly generated group actions", "Harmonic Analysis and Applications," C. Heil, ed., Birkhauser Verlag Basel (2006), 209-230.

    • 2005

  • D.R. Larson, " Decomposition of operators and construction of frames, " Proceedings of the Oberwolfach Math. Institute Mini-Workshop on Wavelets, Frames and Operator Theory, spring (2004).
  • D. Han, D. Larson, Z. Pan and W. Wogen, "Extensions of operators", Indiana J. Math., 53(2004), 1151-1169.
  • K. Dykema, D. Freeman, K. Kornelson, D. Larson, M. Ordower and E. Weber, "Ellipsoidal tight frames and projection decompositions of operators", Illinois J. Math., 48(2004), 477-489..
  • R. Harte and D. Larson, "Skew exactness perturbations", Proc. AMS, 132(2004), 2603-2611.
  • D. Hadwin, D.R. Larson and D. Timotin, "Approximation Theory and Matrix Completions", Linear Algebra and its Appl., 377(2004), 165-179.
  • K. Kornelson and D.R. Larson, "Rank-one decompositions of operators and construction of frames", Contemporary Math., 345(2004), 203-214.
  • A. Aldroubi, D.R. Larson, W-S. Tang and E. Weber, "Geometric aspects of frame representations of abelian groups", Trans. AMS., 356(2004), 4767-4186.
  • D. Hadwin and D.R. Larson, "Completely rank-non-decreasing linear maps", Journal of Functional Analysis, 199(2003), 210-227
  • E. Azoff, E. Ionascu, D.R. Larson and C. Pearcy, "Direct paths of wavelets", Houston J. Math., 29(2003), 737-756.
  • D.R. Larson, W-S. Tang and E. Weber, "Multiwavelets associated with countable abelian groups of unitary operators in Hilbert spaces", Internat. J. Pure and Appl. Math., 06 (2003), 123-144.
  • M. Frank and D.R. Larson, "Frames in Hilbert C*-modules and C*-algebras", Journal of Operator Theory, 48(2002), 273-314.
  • D.R. Larson, W-S. Tang, and E. Weber, "Riesz wavelets and multiresolution structures", SPIE Proceedings Vol. 4478, Wavelet Applications in Signal and Image Processing IX (2001), 254-262.
  • D. Han and D.R. Larson, "Wandering vector multipliers for unitary groups", Transactions AMS, 353(2001), 3347-3370.
  • M. Frank and D.R. Larson, "Modular frames for Hilbert C*-modules and symmetric approximation of frames", SPIE Proceedings Vol. 4119, Wavelet Applications in Signal and Image Processing VIII (2000), 325-336.
  • D. Han and D.R. Larson, "Frames, bases and group representations", Memoirs American Math. Soc. 147 (2000), no. 697. [Note: the pdf file we post here is accurate but is not complete because it is missing some finishing details and results that are included in the published version.]
  • J-P Gabardo, D. Han, and D.R. Larson, "Gabor frames and operator algebras", SPIE Proceedings Vol. 4119, Wavelet Applications in Signal and Image Processing VIII (2000), 337-345.

    • 2000

  • D. Han, D. Larson, M. Papadakis and Th. Stavropoulos, "Multiresolution analysis of abstract Hilbert spaces and wandering subspaces", Contemporary Math., 247(1999), 259-284.
  • P. Casazza, D. Han and D.R. Larson, "Frames for Banach spaces", Contemporary Math., 247 (1999), 149-182.
  • M. Frank and D.R. Larson, "A module frame concept for Hilbert C*-modules", Contemporary Math., 247 (1999), 207-234.
  • E. Ionascu, D.R. Larson and C. Pearcy, "On wavelet sets", J. Fourier Analysis and Applications, 4(1998), 711-721.
  • D.R. Larson and The Wutam Consortium, "Basic Properties of Wavelets", Journal of Fourier Analysis and Applications, 4(1998), 575-594. [The "Wutam Consortium" is a group of researchers based at Washington University (St. Louis) and Texas A&M University (College Station).]
  • X. Dai and D.R. Larson, "Wandering vectors for unitary systems and orthogonal wavelets", Memoirs American Math. Soc. 134 (1998). [Note: the pdf file we post here is accurate but is not complete because it is missing some finishing details and results that are included in the published version.]
  • D. Hadwin and D.R. Larson, "Strong limits of similarities", Operator Theory: Advances and Applications, 104(1998), 139-146.
  • D.R. Larson, "Frames and wavelets from an operator-theoretic point of vies", Contemporary Math., 228 (1998), 201-218.
  • E. Ionascu, D.R. Larson and C. Pearcy, "On the unitary systems affiliated with orthonormal wavelet theory in n-dimensions", Journal of Functional Analysis, 157(1998), 413-431.
  • X. Dai, D.R. Larson and D. Speegle, "Wavelet sets in R^n II", Contemporary Math. 216(1998), 15-40.
  • X. Dai, D.R. Larson, and D. Speegle, "Wavelet sets in R^n", J. Fourier Analysis and Applications, 4(1997), 451-456.
  • D.R. Larson, " Von Neumann algebras and wavelets " , Proc. Nato Adv. Studies Institute on Operator Algebras and Applications (1997), 267-312, Kluwer Acad. Publications.
  • D.R. Larson and B. Solel, "Structured triangular limit algebras", Proc. London Math. Soc., 75(1997), 177-193.
  • T. Hudson, E. Katsoulis and D.R. Larson, "Extreme points in triangular UHF algebras", Transactions AMS, 349(1997), 3391-3400.
  • D.R. Larson and W. Wogen, " Extensions of bitriangular operators, " Int. Eq. Operator Theory 25(1996), 216-223.
  • J. Kraus and D.R. Larson, " Preannihilators, the operator approximation property, and dual products, " J. Operator Theory 36(1996), 21-43.

    • 1995

  • W. Gong, D.R. Larson and W. Wogen, "Two results on separating vectors", Indiana Math. Journal, 43(1994), 1159-1165.
  • D.R. Larson and W. Wogen, " Extensions of normal operators, " Int. Eq. Operator theory 20(1994), 325-334.
  • V. Kaftal, D.R. Larson and G. Weiss, "Quasitriangular subalgebras of semifinite von Neumann algebras are closed", J. Functional Analysis, 107(1992), 387-401.
  • D. Herrero, D. Larson and W. Wogen "Semitriangular operators " , Houston J. Math. 17 (1992), 477-499.
  • D.R. Larson and D. Pitts, " Some questions concerning nest algebras, " Contemp. Math. 120(1991), 89-96.
  • D.R. Larson and W. Wogen , " Some problems on triangular and semitriangular operators, " Contemp. Math. 120(1991), 97-100.
  • D.R. Larson and D. Pitts, " Idempotents in nest algebras, " J. Funct. Anal. 97(1991), 162-193.
  • D.R. Larson and D. Pitts, " Some recent progress in nest algebras, " Proc. Symposia Pure Math. 51(1990), 333-346.
  • G.D. Allen, J. Ward, D.R. Larson and G. Woodward, " Similarity of nests in L1, " J. Funct. Anal. 92(1990), 49-76.
  • D.R. Larson and A. Sourour, " Local derivations and local automorphisms of B(X), " Proc. Symposia Pure Math. 51(1990), 187-194.
  • D .R. Larson and W. Wogen, " Reflexiviy properties of T+0 ", J. Functional Anal. 92(1990), 448-467.

    • 1990

  • D.R. Larson, "Reflexivity, algebraic reflexivity, and linear interpolation", American J. Mathematics, 110(1988), 283-299.
  • D.R. Larson and B. Solel, " Bimodules of nest subalgebras of von Neumann algebras, " Op. Theory Adv. Appl. 32(1988), Birkhauser Verlag Basel, 159-180.
  • D.R. Larson, " On similarity of nest in Hilbert space and in Banach spaces, " Springer-Verlag Lecture Notes in Mathematics Series 1332(1988), 179-194.
  • D.R. Larson, " Triangularity in operator algebras, " Pitman Reseach Notes in Mathematics Series 192(1988), 121-188.
  • D.R. Larson, " Triangularity in operator algebras " , Pitman Res. Notes in Math. Series 192 (1988), 121-188.
  • D.R. Larson, "Hyperreflexivity and a dual product construction", Transactions AMS, 294(1986), 79-88.
  • D.R. Larson and B. Solel, " Nests and inner flows, " J. Operator Theory 16(1986), 157-164.
  • J. Kraus and D.R. Larson, " Reflexivity and distance formulae, " Proc. London Math. Soc. 53 (1986), 340-356.
  • J. Kraus and D.R. Larson, " Some applications of a technique for constructing reflexive operator algebras, " J. Operator Theory 13 (1985), 227-236.
  • D.R. Larson, "Nest algebras and similarity transformations", Annals of Mathematics, 121(1985), 409-427.
  • F. Gilfeather, A. Hopenwasser and D.R. Larson, " Reflexive algebras with finite width lattices: tensor products, cohomology, compact perturbations, " J. Funct. Anal. 55 (1984), 176-199.

    • 1985

  • F. Gilfeather and D.R. Larson, " Nest subalgebras of von Neumann algebras: commutants modulo the Jacobson radical, " J. Operator Theory 10 (1983), 95-118.
  • F. Gilfeather and D.R. Larson, " Commutants modulo the compact operators of certain CSL algebras II, " Integral Eq. and Operator Theory 6 (1983), 345-256.
  • D.R. Larson, " A solution to a problem of J.R. Ringrose, " Bulletin (New Series) AMS 7 (1982), 243-246.
  • F. Gilfeather and D.R. Larson, "Nest subalgebras of von Neumann algebras", Advances in Mathematics, 46(1982), 176-199.
  • D.R. Larson, " Annihilators of operator algebras", Topics in Modern Operator Theory, vol. 6 (1982), Birkhauser, 119-130.
  • F. Gilfeather and D.R. Larson, " Structure in reflexive subspace lattices, " J. London Math. Soc. 26 (1982), 117-131.
  • F. Gilfeather and D.R. Larson, " Nest subalgebras of von Neumann algebras: Commutants modulo compacts and distance estimates , " J. Operator Theory 7 (1982), 279-302.
  • F. Gilfeather and D.R. Larson, " Commutants modulo the compact operators of certain CSL algebras, " Topics in Modern Operator Theory vol. 2 (1981), Birkhauser, 105-120.

    • 1980

  • A. Hopenwasser and D.R. Larson, "The carrier space of a reflexive operator algebra", Pacific J. Math., 81(1979), 417-434.
  • D.R. Larson, " On the structure of certain reflexive algebras," J. Funct. Anal. 31 (1979), 275-292.

    •