# David R. Larson

## Research Interests

Functional
AnalysisOperator
Algebras
and Operator Theory Applied
Harmonic
Analysis Frame Theory
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. arXivV. 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.
arXivA.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.
arXivD.R. Larson and P.
Massopust, "Coxeter groups and wavelet sets,"
Contemp. Math. 451 (2008), 187-218. arXivC.
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.