1. Decompositions of the maximal ideal space of L, Ph.D. Thesis, Michigan State University, 1982.

2. Decompositions of the maximal ideal space of L , Trans. Amer. Math. Soc. 282 (1984) 33-44.

3. Divisibility in Douglas algebras, Michigan Math. J., 31 (1984) 89-94 (with S. Axler).

4. Singular functions and division in H + C, Proc. Amer. Math. Soc. 92 (1984) 268-270.

5. Rotation invariant ideals in subalgebras of L, Proc. Amer. Math. Soc. 95 (1985) 32-36.

6. Prime ideals in closed subalgebras of L, Michigan Math. J. 33 (1986) 315-323.

7. A Beurling Rudin theorem for H, Illinois J. Math 31 (1987) 629-644 ( with H. Hedenmalm and R. Mortini).

8. Functions not vanishing identically on Gleason parts of Douglas algebras, Proc. Amer. Math. Soc. 104 (1988), 1086-1090.

9. Gleason Parts and COP, J. of Functional Analysis 83 (1989) 44-49.

10. F-Ideals and QAB, J. London Math. Soc. (2) 37 (1988) 509-519 (with R. Mortini)

11. Algebras on the disk and doubly commuting multiplication operators, Trans. Amer. Math. Soc. 309 (1988) 711-723. (with S. Axler)

12. Sequences in the maximal ideal space of H, Proc. Amer. Math. Soc. 108 (1990) 731-740. (with S. Axler)

13. Homeomorphic disks in the spectrum of H, Indiana U. Math. J., 39 (1990) 961-983. (with H.-M. Lingenberg and R. Mortini)

14. Bourgain algebras of Douglas algebras, Canadian Journal of Mathematics,44 (1992) 797-804. (with K. Izuchi and R. Mortini)

15. Finitely generated radical ideals in H , Proc. Amer. Math. Soc.116 (1992) 483-488.(with U. Daepp and R. Mortini)

16. Algebras of bounded functions on the disc, Proceedings Conference on Function Spaces, Lecture Notes in Pure and Applied Mathematics Series/136, Marcel Dekker, 1992.

17. Some counterexamples in subalgebras of L, Indiana University Math. J., 40, (1991) 1301 - 1313. (with K. Izuchi)

18. Interpolating Blaschke products and factorization in Douglas algebras, Mich. Math. J., 38 (1991) 147-160. (with R. Mortini)

19. Composition of inner functions, Results in Mathematics, 25 (1994) 252 - 269. ( with L. Laroco, R. Mortini, and R. Rupp)

20. Results on antisymmetric sets and a question about Gleason parts, Linear and Complex Analysis Problem Book 3, Part I, Springer-Verlag, (1994) 119-121.

21. The Generalized Corona Theorem, Math. Ann. 301 (1995) 135-154 ( with A. Nicolau and R. Mortini)

22. On the Corona Theorem, Function spaces the second conference, Lecture Notes in Pure and Applied Mathematics Series/172, Marcel Dekker (1995), 147-165. (with R. Mortini)

23. Bourgain algebras on the maximal ideal space of H, Rocky Mountain J. Math. 25 (1995), 1025-1051. (with K. Izuchi)

24. Alling's Conjecture on Prime Ideals, J. Functional Analysis, 148 (1997), 185-190. (with R. Mortini)

25. Hankel Type Operators, Bourgain Algebras, and Uniform Algebras, Holomorphic Spaces, MSRI Publications, 33 (1998).

26. Harmonic Extensions and the Böttchner-Silbermann Conjecture, Studia Math., 127 (1998) 3, 201-222. (with D. Zheng)

27. A Survey of Closed Ideals in Familiar Functions Algebras , Function spaces (Edwardsville, IL, 1998), 161--170, Contemp. Math., 232, Amer. Math. Soc., Providence, RI, 1999. (with R. Mortini)

28. Essentially commuting Toepiltz operators , Pacific Math. J., 190 (1999), 1, 87--109. (with D. Zheng)

29. Division theorems and the Shilov property in H + C, Pacific J. Math. 189 (1999), 2, 279--292. (with R. Mortini)

30. Higher Order Hulls in H II, J. Funct. Analysis, 177 (2000), 1, 107 - 129. (with K. Izuchi and R. Mortini)

31. Hankel Type Operators on Bounded Analytic Functions, Trans. Amer. Math Soc., 352 (2000), 1, 363--377. (with J. Dudziak and T. Gamelin)

32. An upper bound for the distance to finitely generated ideals in Douglas Algebras, Studia Math. 148 (1) 2001. (with R. Mortini and D. Suarez).

33. Localisation techniques for division in Douglas algebras, Math. Proc. R. Ir. Acad. 101A (2001), 1, 49--60. (with R. Mortini and D. Suarez)

34. Ellipses and finite Blaschke products, Amer. Math. Monthly 109 (2002), 9, 785--795. (with U. Daepp and R. Mortini)

35. k-hulls and support sets in the spectrum of H + C, Archiv der Mathematik, 79, 1 (2002) 51--60. (with R. Mortini)

36. Sequences separating fibers in the spectrum of H, Topology Appl. 129 (2003), 3, 221--238. (with K. Izuchi and R. Mortini)

37. Hulls of closed prime ideals in H, Illinois J. Math. 46 (2002), 2, 519--532. (with R. Mortini)

38. Universal Blaschke Products, Math. Proc. Cambridge Philos. Soc. 136 (2004), 1, 175--184. (with R. Mortini)

39. Asymptotic interpolating sequences in uniform algebras, J. London Math. Soc., 67 (2003), 2, 481-498. (with R. Mortini)

40. Homotopic composition operators on H (B^n), Proceeding of the Fourth Conference, Contemp. Math., 177--188, Amer. Math. Soc., Providence, RI, 2003. (with D. Suarez and R. Mortini)

41. Essential norms of composition operators, Integral Eqn. and Op. Theory, 48 (2004), 1, 27--40. (with B. MacCluer)

42. Universal singular inner functions, Canadian Math. Bulletin, 47 (2004), 1, 17--21. (with R. Mortini)

43. The Dirichlet Problem on Quadratic Surfaces, Mathematics of Computation, 73 (2004), 637--651. (with S. Axler and K. Voss)

44. Alice in Switzerland: The Life and Mathematics of Alice Roth, Math. Intelligencer 27 (2005), 1, 41--54. (with U. Daepp, P. Gauthier, G. Schmieder)

45. Dirichlet: his life, his principle, and his problem. Math. Mag. 78 (2005), 4, 283--296. (with J. Smith*)

46. Cluster sets of interpolating Blaschke products, Cluster sets of interpolating Blaschke products. J. Anal. Math. 96 (2005), 369--395. (with R. Mortini)

47. Radial limits of interpolating Blaschke products, Math. Ann., 331 (2005), 2, 417--444 (with R. Mortini)

48. Value distribution of interpolating Blaschke products, J. London Math. Soc. (2) 72 (2005), 1, 151--168. (with R. Mortini)

49. Countably generated prime ideals, Math. Z. 251 (2005), 523-533. (with R. Mortini)

50. Norms and essential norms of linear combinations of endomorphisms, Trans. Amer. Math. Soc. 358 (2006), no. 2, 553--571 (with R. Mortini)

51. Infinite dimensional vector spaces of universal functions for H of the ball, Canadian Math. Bull., 50 (2007), no. 2, 172--181. (with R. Aron)

52. Boundary interpolation by finite Blaschke products. Constr. Approx. 27 (2008), no. 1, 75--98. (with R. C. Rhoades*)

53. How to get universal functions, Math. Ann. 337 (2007), 4, 875--886. (with F. Bayart)

54. On some representation formulas involving moduli of Blaschke products, Analysis (Special edition dedicated to Gerald Schmieder), Analysis 27 (2007), 261-272. (with A. Gluchoff and R. Mortini)

55. Bounded universal functions for sequences of holomorphic self-maps of the disk. Ark. Mat. 47 (2009), no. 2, 205--229. (with F. Bayart, S. Grivaux, and R. Mortini)

56. Norm controlled inversions and a Corona Theorem for H-quotient
algebras, J. Funct. Analysis 255 (2008), 854-876. (with N. Nikolski, R. Mortini)  

57. Bounded universal functions in one and several complex variables. Math. Z. 258 (2008), no. 4, 745--762. (with F. Leon-Saavedra, R. Mortini)

58. Two new characterizations of Carleson-Newman Blaschke products, Israel J. Math.,77 (2010), 267--284. (with R. Mortini)

59. Cyclic Blaschke products for composition operators, Rev. Mat. Iberoam. 25 (2009), no. 2, 447--470. (with E. Gallardo-Gutierrez)

60. Numerical ranges of restricted shifts and unitary dilations. Oper. Matrices 3 (2009), no. 2, 271--281. (with I. Chalendar and J. R. Partington)

61. Boundary interpolation and approximation by infinite Blaschke products. Math. Scand. 107 (2010), no. 2, 305–319. (with I. Chalendar and J. R. Partington)

62. Poncelet's theorem, Sendov's conjecture, and Blaschke products. J. Math. Anal. Appl. 365 (2010), no. 1, 93--102. (with K. Voss and U. Daepp)

63. Minimal invariant subspaces for composition operators, J. Math. Pures Appl. (9) 95 (2011), no. 3, 245–25. (with E. Gallardo-Gutierrez)

64.The group of invariants of an inner function with finite spectrum, JMAA, 389 (2012), 1259--1267. (with I. Chalendar and J. R. Partington).

65. Pervasive algebras and maximal subalgebras, Studia Mathematica, to appear. (with Anthony G. O'Farrell)

66. Determination of inner functions by their value sets on the circle, Computational Methods and Function theory, 11 (2011), 353-373. (with I. Chalendar and J. R. Partington)

67.. Polynomials, Ellipses, and Matrices: Two questions, one answer, Amer. Math. Monthly, Volume 118, Number 6, June 2011 , pp. 522-533 (12). (with Elisabeth Skubak*)

68. Numerical ranges of contractions with finite defects, Integral Equations & Operator Theory, 70 (2011), no. 2, 265–279. (with C. Benhida and D. Timotin)

69. Approximation by polynomials and Blaschke products having all zeros on a circle, Illinois J. Mathematics, to appear. (with David Farmer)

70. Orbits of non-elliptic disk automorphisms on H^p, JMAA., to appear. (with E. Gallardo-Gutierrez and Daniel Suarez)

71. Interpolating Blaschke products and angular derivatives, Trans. AMS, posted January 3, 2012 (online). (with E. Gallardo-Gutierrez)

* indicates publication together with Bucknell student

Books

Reading, Writing, and Proving: A Closer Look at Mathematics, Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2003, (with U. Daepp).

Now in its second edition! Reading, Writing, and Proving: A Closer Look at Mathematics, Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2011, Second Edition (with U. Daepp).

Book/DVD Reviews

Imagining Numbers (particularly the square root of -15), by Barry Mazur, Math. Intelligencer, Mathematical Intelligencer, 2007; 29 (1), p. 52.

Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills, by Paul J. Nahin, Math. Intelligencer, Mathematical Intelligencer, 2007; 29 (3), p. 69-70.

The Great Pie Debate, starring Collin Adams, Thomas Garrity, Edward Burger, Mathematical Intelligencer, 2008; 30 (2), p. 71.

Fearless Symmetry, by Avner Ash, Robert Gross, Mathematical Intelligencer, 2008; 30 (1), p. 71-72.

Figuring it out, by Nuno Crato, Mathematical Intelligencer, to appear.

Bull. London Math. Soc. Representation theorems in Hardy spaces, (London Mathematical Society Student Texts 74), Javad Mashreghi: 372 pp., isbn 978-0-521-73201-7 (P), 978-0-521-51768-3 (H) 5 (Cambridge University Press, Cambridge, 2009).

Mathematical Reviews, [MR2458901], Review of Kaniuth, Eberhard, FA course in commutative Banach algebras. Graduate Texts in Mathematics, 246. Springer, New York, 2009. xii+353 pp. $69.95. ISBN 978-0-387-72475-1.

Student Stuff

Sendov's conjecture, by Andrew Shaffer (extract the file and use Sendov Plotter)