Joel H. Shapiro


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Volterra Adventures, (book, 219 p) AMS Student Mathematical Library #85, American Math. Society 2018.

A Fixed-Point Farrago, (book, 221p) Springer 2016.

Strongly compact algebras associated with composition operators
New York J. Math. 18 (2012) 849-875.

Composition operators ♥ Toeplitz operators, in: Five Lectures in Complex Analysis, Contemporary Mathematics, vol. 525, Amer. Math. Soc., Providence, RI, 2010, pp. 117-139.

Eigenfunctions for hyperbolic composition operators–redux
Operator Theory: Advances and Applications 202 (2010) 519–534.

Intertwining relations and extended eigenvalues for analytic Toeplitz operators (with Paul S. Bourdon), Illinois J. Math. 52 (2008) 1007–1030.

Adjoints of rationally induced composition operators (with Paul S.Bourdon)
J. Functional Analysis 255 (2008) 1995–2012.

On the outputs of linear control systems, J. Math. Anal. Appl., 340 (2008) 116–125.

Every composition operator is (mean) asymptotically Toeplitz
J. Math. Anal. Appl. 333 (2007) 523–529.

On the toeplitzness of composition operators (with Fedor Nazarov)
Complex Variables and Elliptic Eqns. 52 (2007),193–210.

On convergence to the Denjoy-Wolff Point (with Paul S. Bourdon and Valentin Matache)
Illinois J. Math. 49 (2005) 405–430.

Some properties of N-supercyclic operators (with Paul S. Bourdon and Nathan Feldman)
Studia Mathematica 165 (2) (2004) 135–157.

Hardy spaces that support no compact composition operators (with Wayne Smith)
J. Functional Analysis 205 (2003) 62–89.

Which linear-fractional composition operators are essentially normal? (with Paul S. Bourdon, David Levi, and Sivaram K. Narayan), J. Math. Anal. Appl. 280 (2003) 30–53.

When is zero in the numerical range of a composition operator? (with Paul S. Bourdon)
Integral Equations and Operator Theory 44 (2002) 401–441.

Decomposability and the cyclic behavior of parabolic composition operators, in: Recent Progress in Functional Analysis, Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia, Valencia, Spain, July 3-7, 2000, K.D. Bierstedt, J. Bonet, M. Maestre, J. Schmets (ed.), North-Holland Math. Studies, 2001.

The numerical ranges of automorphic composition operators (with Paul S. Bourdon)
J. Math. Analysis and Appl. 251 (2000) 839-854.

Hypercyclic operators that commute with the Bergman backward shift (with Paul S. Bourdon)
Trans. Amer. Math. Soc. 352 (2000) 5293–5316.

Compact Composition operators on the Smirnov class (with Jun Soo Choa and Hong Oh Kim)
Proc. Amer. Math. Soc. 128 (2000) 2297–2308, MR 2000k:47034.

What do composition operators know about inner functions?
Monatshefte für Mathematik 130 (2000) 57–70.

Simple Connectivity and Linear Chaos, Rend. Circ. Mat. Palermo, Ser. II, Suppl. 56 (1998) 27–48.

Composition operators and Schroeder’s functional equation,
Contemp. Math. 213 (1998), 213–228, MR 98m:47048.

Riesz composition operators (with Paul S. Bourdon)
Pacific J. Math. 181 (1997), 231–245, MR 98j:47068.

Cyclic Phenomena for Composition Operators (with Paul S. Bourdon), Memoirs of the American Math. Society #596, Vol. 125, 1997, pp.1–105, American Math. Society, Providence, R.I., January 1997. MR 97h:47023 (Featured Review).

Geometric models and compactness of composition operators (with David A. Stegenga and Wayne Smith), J. Functional Analysis 127 (1995) 21–62, MR 95m:47051 (Featured Review).

Composition Operators and Classical Function Theory,
Springer Verlag, New York, 1993 MR 94k:47049.

Random Dirichlet functions: multipliers and smoothness (with G. Cochran and D. Ullrich)
Canadian J. Math. 45 (2) 1993, 255–268. MR 94f:30001.

The cyclic behavior of translation operators on Hilbert spaces of entire functions (with Kit Chan), Indiana Univ. Math. J. 40 (1991) 1421–1449. MR 92m:47060.

Cyclic composition operators on H2 (with Paul S. Bourdon) Operator Theory: Operator Algebras and Applications (Durham, N.H. 1988) 43–55, Proc. Sympos. Pure Math. Part 2, American Math. Soc. 51 (1990) (Summary of first part of Cyclic Phenomena for Composition Operators, above). MR 91h:47028

Operators with dense, invariant cyclic vector manifolds (with Gilles Godefroy)
J. Functional Analysis 98 (1991) 229–269. MR 92d:47029

Isolation amongst the composition operators (with Carl Sundberg)
Pacific J. Math. 145 (1990), 117–152. MR 92g:47041

Compact composition operators on L1 (with Carl Sundberg)
Proc. Amer. Math. Soc. 108 (1990), 443–449. MR 90d:47035

Spectral synthesis and common cyclic vectors (with Paul S. Bourdon)
Michigan Math. J. 37 (1990), 71–90. MR 91m:47039

Fourier series, mean Lipschitz spaces, and bounded mean oscillation (with Paul S. Bourdon and W. T. Sledd) In Analysis at Urbana, Vol. 1: Proceedings of the Illinois Special Year in Analysis, pp 81 – 110. Cambridge Univ. Press, 1989. MR 90j:42011

Cluster set, essential range, and distance estimates in BMO
Michigan Math. J. 34 (1987), 323–336. MR 89b:30029

Universal vectors for operators on spaces of holomorphic functions (with R.M. Gethner),
Proc. Amer. Math. Soc. 100 (1987), 281–188. MR 88g:47060

Compact composition operators on spaces of boundary-regular holomorphic functions
Proc. Amer. Math. Soc. 100 (1987)  49–57. MR 88c:47059

The essential norm of a composition operator, Annals of Math. 125 (1987) 375–404. MR 88c:47058

Angular derivatives and compact composition operators on the Hardy and Bergman spaces (with B. D. MacCluer), Canadian J. Math. 38 (1986) 878–906. MR 87h:47048

Putnam’s theorem, Alexander’s spectral area estimate, and VMO (with Sheldon Axler)
Math. Annalen 271 (1985) 161–183. MR 87b:30053

Linear topological properties of the harmonic Hardy spaces hp for 0 < p < 1, Illinois J. Math. 29 (1985) 311–339. MR 86f:46023

Tangential boundary behavior of harmonic extensions of Lp potentials (with A. Nagel and W. Rudin), Proceedings of harmonic analysis conference in honor of Antoni Zygmund, Wadsworth 1983, 533–548 (Summary of the next paper). MR 85e:31002

Tangential boundary behavior of functions in Dirichlet-type spaces (with A. Nagel and W. Rudin)
Annals of Math. 116 (1982) 331–360. MR 84a:31002

Hausdorff measure and Carleson thin sets,
Proc. Amer. Math. Soc. 79 (1980) 67–72. MR 81m:28001

Cauchy transforms and Beurling-Carleson-Hayman thin sets,
Michigan Math. J. 27 (1980) 339–351. MR 82b:30039

Zeros of random functions in Bergman spaces
Ann. Inst. Fourier (Grenoble) 29 (1979) 159–171. MR 81 h:30054

Subspaces of Lp(G) spanned by characters: 0 < p < 1
Israel J. Math. 29 (1978) 248–264. MR 57:17123

Zeros of functions in weighted Bergman spaces, Michigan Math. J. 24 (1977) 243–256. MR 57:3404

Remarks on F-spaces of analytic functions, Springer Lecture Notes # 604 (1977) 107–124. (Survey article in: Proceedings of NSF-CBMS Conference on Banach Spaces of Analytic Functions, Kent State University, July 1976.) MR 58:7050

Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Bergman spaces
Duke Math. J. 43 (1976) 187–202. MR 58:17806

Unusual topological properties of the Nevanlinna Class (with Allen L. Shields)
American J. Math. 97 (1976) 915–936. MR 52:11053

Bases and basic sequences in F-spaces (with N.J. Kalton)
Studia Math. 56 (1976) 47–61. MR 54:8215

An F-space with trivial dual and non-trivial compact endomorphisms (with N.J. Kalton)
Israel J. Math. 20 (1975) 282–291. MR 53:6271

On the weak basis theorem in F-spaces, Canadian J. Math. 26 (1974) 1294–1300. MR 50:7990

Compact, nuclear, and Hilbert-Schmidt composition operators on H2 (with P.D. Taylor)
Indiana Univ. Math. J. 23 (1973) 471–496. MR 48:4816

Non-coincidence of the strict and strong operator topologies
Proc. Amer. Math. Soc. 35 (1972) 81–87. MR 46:6000

On convexity and compactness in F-spaces with bases
Indiana Univ. Math. J. 21 (1972) 1073–1090. MR 45:4105

The bounded weak star topology and the general strict topology
J. Functional Analysis 8 (1971) 275–286. MR 44:7294

Weak topologies on subspaces of C(S), Trans. Amer. Math. Soc. 157 (1971) 471–479. MR 54:3375

Extension of linear functionals on F-spaces with bases
Duke Math. J. 37 (1970) 639–645. MR 42:5004

Nonconvex linear topologies with the Hahn Banach extension property, (with David A. Gregory)
Proc. Amer. Math. Soc. 25 (1970) 902–905. MR 41:8957

Examples of proper, closed, weakly dense subspaces in nonlocally convex F-spaces
Israel J. Math. 7 (1969) 369–380. MR 41:2346