Bibliography

Analysis and Geometry on Trees

Recent Articles

  1. Range of the horocyclic Radon Transform on Trees, (with E. Casadio Tarabusi and F. Colonna), Ann. Inst. Fourier Grenoble, 50(2000), 211-234.
  2. The Distribution-Valued Horocyclic Radon Transform on Trees, (with E. Casadio Tarabusi and F. Colonna), Harmonic Analiysis and Integral Geometry, Research Notes in Math. 422(2001), Chapman & Hall/CRC , 55-66.
  3. Polyharmonic Functions on Trees, (with Flavia Colonna, Kohur GowriSankaran, and David Singman), American Journal of Mathematics, 124(2002), 999-1043.
  4. Analytic Eigendistributions and applications to homogeneous trees, (with Flavia Colonna), Advances in App. Math., 29(2002), 539-562.
  5. A sequence of polynomials for studying production functions, (with Margherita Barile), J. Pure and App. Alg., 185(2003), 35-42.
  6. Trees as Brelot Spaces, (with Ibtesam Bajunaid, Flavia Colonna, and David Singman), Advances in App. Math., 30(2003), 706-745.
  7. An inversion formula for finding technology distribution for production functions, (with Mauro Pagliacci), Advances in App. Math., 33(2004), 476-486. 
  8. Distributions and Measure on the Boundary of a Tree, (with Flavia Colonna, and David Singman),  J. Math. Anal. and App, 293(2004), 89-107. 
  9. Function series, Catalan numbers, and random walks on trees, (with Ibtesam Bajunaid, Flavia Colonna, and David Singman), Amer. Math. Monthly, 112(2005), 765-785.*
  10. Preimages of One-point sets of Bloch and normal functions, (with Flavia Colonna), Med. J. of Math, 3(2006), 513-532.
  11. A global Riesz decomposition theorem on trees without positive potentials, (with Flavia Colonna, and David Singman), J. London Math. Society, 75(2007), 1-17.
  12. Isometric composition operators on the Bloch space in the polydisk, (with Flavia Colonna), in Banach Spaces of Analytic Functions, Contemp. Math., 454(2008), 9-21.
  13. A Riesz decomposition theorem on harmonic spaces without positive potentials, (with Flavia Colonna, and David Singman) Hiroshima Math. J. 38 (2008), 37-50.
  14. Radial Heat Diffusion from the Root of a Homogeneous Tree and the Combinatorics of Paths, (with Mauro Pagliacci and Massimo Picardello), Bolletino Unione Matematica Italiana  (9)I (2008), 619-628.
  15. Biharmonic Green functions on homogeneous trees, (with Flavia Colonna and David Singman), Mediterranean Journal of Mathematics, 6(2009), 249-271.
  16. Classification of harmonic structures on graphs, with Ibtesam Bajunaid, David Singman, Flavia Colonna, Advances in Applied Mathematics 43 (2009), no. 2, 113-136.
  17. Biharmonic extensions on trees without positive potentials, with Ibtesam Bajunaid, Flavia Colonna,  and David Singman, Journal of Mathematical Analysis and Applications (378) 2011,710-722.
  18. Carleson measures on a homogeneous tree, with Joel Cohen and Flavia Colonna, Journal of Mathematical Analysis and Applications, 395(2012), 403-412.
  19. Carleson and vanishing Carleson measures on radial trees, with David Singman and Flavia Colonna, Mediterranean Journal of Mathematics, 10(2013), 1233-1256.

       * Winner of 2006 Lester R. Ford award

Selected Earlier Articles

  1. The Equivalence of Two Concepts of Categorical Grammar, Information and Control, 10 (1967), 475-484.
  2. The Decomposition of Stable Homotopy, Ann. of Math., 87 (1968), 305-320.
  3. A Spectral Sequence Automorphism Theorem: Applications to Fibre Spaces and Stable Homotopy, Topology 7 (1968), 173-177.
  4. Coherent Graded Rings and the Non-Existence of Spaces of Finite Stable Homotopy Type, Comment. Math. Helv. 44 (1969), 217-228.
  5. A Note on Homological Dimension, Journal of Algebra 11 (1969), 483-487.
  6. Stacked Bases for Modules over Principal Ideal Domains, (with H. Gluck), Journal of Algebra 14 (1970), 493-505.
  7. The Hurewicz Homomorphism on MU, Invent. Math. 10 (1970), 177-186.
  8. Clarification to a result in "A Spectral Sequence Automorphism Theorem ...", Topology 9 (1970), 299-300.
  9. Poincaré 2-Complexes I, Topology 11 (1972), 417-419.
  10. The Homotopy Groups of Inverse Limits, Proc. London Math Soc. (3) 27 (1973), 159-177.
  11. Inverse Limits of Principal Fibrations, Proc. London Math Soc. (3) 27 (1973), 178-192.
  12. The Commutator Subgroup Made Abelian, Proc. AMS 38 (1973), 507-508.
  13. Zero Divisors in Group Rings, Comm. in Algebra 2 (1974), 1-14.
  14. Homotopy Surfaces, Topology 14 (1975), 23-28.
  15. Complexes Dominated by a 2-Complex, Topology 16 (1977), 409-415.
  16. Caratteristica di Eulero a Valori Reali, Rend. Sem. Mat. Fis. Milano XLVII (1977), 233-239.
  17. Complexes of Cohomological Dimension 2, Proc. Symp. Pure Math. 32 (1978), 221-223.
  18. On the Number of Generators of a Module, J. Pure and App. Algebra 12 (1978), 15-19.
  19. Aspherical 2-Complexes, J. Pure and App. Algebra 12 (1978), 101-110.
  20. Poincaré 2-Complexes II, Chinese J. of Math. 6 (1978), 25-44.
  21. Finite Group Actions on Finite Complexes, J. Pure and App. Algebra 13 (1978), 9-11.
  22. C*-Algebras Without Idempotents, J. of Funct. Analysis 33 (1979), 211-216.
  23. Von Neumann Dimension and the Homology of Covering Spaces, Quarterly Journal of Mathematics 30 (1979), 133-142.
  24. The Real-Valued Euler Characteristic, Rend. Sem. Mat. Univ. Politec. Torino 39 (1981), 37-48.
  25. Operator Norms on Free Groups, Boll. Un. Mat. Ital. (6) 1-B (1982), 1055-1065.
  26. Cogrowth and Amenability of Discrete Groups, J. Funct. Anal. 48 (1982), 301-309.
  27. C*-Algebras of Abelian Groups, J. Pure and App. Algebra 33 (1984), 7-10.
  28. Radial Functions on Free Products, J. Funct. Anal. 59 (1984), 167-174.
  29. Orthogonal Polynomials with a Constant Recursion Formula and an Application to Harmonic Analysis, (with A. R. Trenholme), J. Funct. Anal. 59 (1984), 175-184.
  30. Idempotents in the reduced C*-algebra of the free group, (with A. Figa'-Talamanca), Proc. A.M.S., 102(1988), 779-782.
  31. Spherical Functions for Abstract Operators, J. Austr. Math. Soc.(A), 45(1988), 195-203.
  32. The 2-Circle and 2-Disk Problems on Trees, (with M.A. Picardello), Israel J. Math., 64(1988), 73-86.
  33. Monotone Multiplicative Functions, Amer. Math. Monthly, 96(1989), 512-513.

Monographs and Proceedings

  1. Stable Homotopy, Lecture Notes in Mathematics, vol. 165, Springer Verlag, Heidelberg-Berlin-New York, 1970.
  2. Successioni Spettrali e Teorie Omologiche Generalizzate, Quaderni del C.N.R., Rome 1978.
  3. Introduzione alla Topologia Algebrica, (with F. Colonna), EdiTel, Rende, 1991.
  4. The Non-Existence of Spaces with Finitely Generated Stable Homotopy, Proc. U.I.C.C. Conf. on Alg. Top. 1968.
  5. The Homotopy Theory of Inverse Limits, Proc. Conf. on Algebraic Topology, Aarhus, 1970
  6. Complexes of Cohomological Dimension Two, Proc. AMS Symp. in Pure Math. 32 (1978), 221-223.
  7. The Radial Fourier-Stieltjes Algebra of Free Groups, (with L. DeMichele), Contemp. Math. 10 (1982), 33-40.

  8.  L2-Cohomology in Topology, Algebra, and Analysis, Proc. 3rd National Meeting on Topology, Trieste, 1986.

  9.  Curvature of Submanifolds,  (with Stanley Zoltek), in Seminars in Geometry, 1 (ed. D. Struppa), EdiTel, Rende, 1987
Analysis and Geometry on Trees
  1. Operator Norms on Free Groups, Boll. Un. Mat. Ital. (6) 1-B (1982), 1055-1065.
  2. Idempotents in the reduced C*-algebra of the free group, (with A. Figa'-Talamanca), Proc. A.M.S., 102(1988), 779-782.
  3. The 2-Circle and 2-Disk Problems on Trees, (with M.A. Picardello), Israel J. Math., 64(1988), 73-86.
  4. Integral Geometry on Trees, (with M.A. Picardello, C.A. Berenstein, and E. Casadio Tarabusi), American Journal of Math., 113(1991), 441-470.
  5. The Horocyclic Radon Transformation on non-homogeneous Trees, (with M.A. Picardello and E. Casadio Tarabusi), Israel J. Math. 78(1992), 363-380.
  6. Characterization of the range and functional analysis of the X-ray transform on trees, (with Flavia Colonna, Enrico Casadio Tarabusi and Massimo Picardello), C.R. Acad. Sci. Paris, 316(I) (1993), 559-564.
  7. The functional analysis of the X-ray transform on trees, (with Flavia Colonna), Advances in App. Math. 14(1993), 123-138.
  8. Range of the X-ray transform on trees, (with M.A. Picardello and E. Casadio Tarabusi), Advances in Math., 22(1994), 153-167.
  9. The Bloch space of a homogeneous tree, (with Flavia Colonna), Bol. Soc. Mat. Mex., 37(1992),63-82.
  10. Embeddings of trees in the hyperbolic disk, (with Flavia Colonna), Complex Variables Theory and Applications, 24(1994), 311-335.
  11. Explicit solutions for the wave equation on homogeneous trees, (with Mauro Pagliacci), Advances in App. Math., 15(1994), 390-403.
  12. Extreme points of the Bloch space of a homogeneous tree, (with Flavia Colonna), Israel J. of Math., 94(1996), 247-271.
  13. Image recovery from exponential blurring, (with Flavia Colonna and Massimo Picardello), Circuits, Systems, and Signal Processing, 15(1996), 261-274.
  14. Eigenfunctions of the Laplacian on a homogeneous tree, (with Flavia Colonna), Contemporary Mathematics 206(1997), Harmonic Functions on Trees and Buildings, 121-124.
  15. Spectral analysis on homogeneous trees, (with Flavia Colonna), Advances in App. Math., 20(1998), 253-274.
  16. Converse mean value theorems on trees and symmetric spaces, (with Enrico Casadio Tarabusi, Massimo Picardello, and Adam Korányi), Journal of Lie Theory,  8(1998), 229-254.
  17. Characterization of the range of the Radon Transformation on Homogeneous Trees, (with E. Casadio Tarabusi and F. Colonna), ERA of the AMS, 5(1999), 11-17.
  18. Range of the horocyclic Radon Transform on Trees, (with E. Casadio Tarabusi and F. Colonna), Ann. Inst. Fourier Grenoble, 50(2000), 211-234.
  19. The Distribution-Valued Horocyclic Radon Transform on Trees, (with E. Casadio Tarabusi and F. Colonna), Harmonic Analiysis and Integral Geometry, Research Notes in Math. 422(2001), Chapman & Hall/CRC , 55-66.
  20. Polyharmonic Functions on Trees, (with Flavia Colonna, Kohur GowriSankaran, and David Singman), American Journal of Mathematics, 124(2002), 999-1043.
  21. Analytic Eigendistributions and applications to homogeneous trees, (with Flavia Colonna), Advances in App. Math., 29(2002), 539-562.
  22. Trees as Brelot Spaces, (with Ibtesam Bajunaid, Flavia Colonna, and David Singman), Advances in App. Math., 30(2003), 706-745.
  23. Distributions and Measure on the Boundary of a Tree, (with Flavia Colonna, and David Singman),  J. Math. Anal. and App, 293(2004), 89-107. 
  24. Function series, Catalan numbers, and random walks on trees, (with Ibtesam Bajunaid, Flavia Colonna, and David Singman), Amer. Math. Monthly, 112(2005), 765-785.