University of Stockholm - Filosofiska Graden 1970
The degree in question "Filosofiska Graden" is a degree above PhD. It often represented 3 or more years of research after PhD. The degree has ceased to exist.
Doctoral advisor: Hans Rådstrom
Investigations on Hilbert's fifth problem for non locally compact groups. Dissertation, Stockholm University, 1970.
Scottish Book - Professor S. Mazur 1972
Description: I received in 1972 a live goose from Professor S. Mazur, Warsaw for the solution of ”The Approximation Problem”. This was the most significant prize offered in the Scottish Book. The Scottish Book is a collection of 193 problems, "important for the development of functional analysis and other branches of mathematics". The Scottish Book is ”one the the most revered relics of the mathematical world”. It was created in the years 1935-1941 by the Polish School. The prize was offered by Mazur in 1936 and the 1972 ceremony is referred to as ”a major media event” in the biography of Stefan Banach by R. Kaluża (1995).
History of Mathematics over 1000 years - IBM 1978
Description: My solution of ”The Basis Problem” is one of approx. 50 contributions to Mathematics in the 20th century reported on IBM's poster IMPORTANT MATHEMATICIANS - A Historical Survey from Year 1000 to 1900.
History of Mathematics over last 75 years - 75th Anniversary of the American Math.Soc. 1991
Description: My solution of ”The Basis Problem” is one of 22 contributions to Mathematics reported on by Prof. P. Halmos in his 1990 survey of the Development of Mathematics in the last 75 years, written for the 75th Anniversary of the American Math.Soc. [see pages 585-586 in Paul R. Halmos, Has progress in mathematics slowed down?, American Mathematical Monthly, v.97 n.7, p.561-588, Aug./Sep. 1990]
Biography - ”Beginning Functional Analysis” 2001
Description: I am one of nine ”key players in the development of functional analysis” given biographies in Prof. K. Saxe's textbook ”Beginning Functional Analysis” (2001). The other eight are: Joseph Fourier (1768-1830), David Hilbert (1862-1943), Henri Lebesgue (1875-1941), René- Maurice Fréchet (1878-1973), Frigyes Riesz (1880-1956), Stefan Banach (1892-1945), Marshall Stone (1903-1989) and John von Neumann (1903-1957). My solution of ”The Invariant Subspace Problem” is referred to as ”his most famous mathematical contribution thus far”.
The Distinguished Scholar Award - Kent State University 2005. Three Distinguished Scholar Awards (DSA) are given annually for outstanding research and/or creative activities by tenured/tenure-track faculty members at Kent State University.
Per Enflo ■ Publications ■ Presentations ■ CV
A simple reason, why Neandertal ancestry can be consistent with current DNA information
Reproduction strategy as a driving force for Human Evolution
Minimal points and contractive projections. Constructive Theory of Functions, Marin Drinov Publishing House (2006), 98-103
Some aspects of the Invariant Subspace Problem (with Lomonosov) Handbook of the Geometry of Banach Spaces, Elsevier Science 2001, Vol. 1, Ch. 13, p. 535-559
Modeling the effects of nutrient concentrations on community production and ecosystem stability: Framework for a Great Lakes Model. (with R.T.Heath, R.Sturtevant and D.Shoup). In Great Lakes Modeling Summit--Focus on Lake Erie. L.Tulen and J.dePinto, Eds., published by Int. Joint Commission, Windsor, ONT., ISBN 1-894280-17-2 (2000), 37-50
Funktionalanalys. Mellan himmel & jord. (1985) 101-105, Stockholm: Infoavdeln., KTH
1. On the nonexistence of uniform homeomorphisms between Lp -spaces. Ark. Mat. 8 (1969) 103-105
2. On a problem of Smirnov. Ark. Math. 8 (1969) 107-109
3. Topological groups in which multiplication on one side is differentiable or linear. Math. Scand. 24 (1969) 195-207
4. Uniform structures and square roots in topological groups. Israel J. Math. 8 (1970) 230-272
5. Investigations on Hilbert's fifth problem for non locally compact groups. Dissertation, Stockholm University, 1970
6. Banach spaces which can be given an equivalent uniformly convex norm. Israel. J. Math., 13
7. A counterexample to the approximation problem in Banach spaces, Acta Mathematica (1973) 130, Number 1, 309-317
8. A Banach space with basis constant greater than 1. Ark Mat. 11 (1973) 103-107
9. Some results concerning Lp(μ)-spaces (with H.P. Rosenthal), J. Funct. Anal. 14(1973), 325-348
10. On the "Three Space Problem" (with J. Lindenstrauss and G. Pisier) Math. Scand. 36 (1975), 199-210
11. On the invariant subspace problem in Banach spaces, Seminaire Maurey-Schwartz (1975-76)
12. On the structure of separable lp spaces (1 < p < oo) (with D. Alspach and E. Odell) Studia Math., 60 (1977), 79-90
13. On infinite-dimensional topological groups. Séminaire Analyse fonctionnelle (dit "Maurey-
Schwartz") (1977-1978), Exposé No. 10 et 11, 11 p.
14. Subspaces of L1 containing L1. (with T. Starbird) Studia Math. 65. 203- 225 (1979)
15. Perturbations at the vertex of an acoustic sawtooth wave in a slightly dispersive medium (with Enflo, B. O.) Report/Institut Mittag-Leffler, 99-0178853-6 ; 1982:1 Stockholm
16. Theoremes de point fixe et d'approximation (with B. Beauzamy); Ark. Mat. Vol. 23 no. 1 (1985): 19-34
17. Estimations de produits de polynomes, (with B. Beauzamy) J. of Number Theory, 21-3 (1985), pp. 390-412
18. Funktionalanalys. Mellan himmel & jord. (1985) 101-105, Stockholm: Infoavdeln., KTH
19. On the invariant subspace problem in Banach spaces; Mittag-Leffler report (1980), Acta Math. Vol. 158, (1987): 213-313
20. An exact solution formula for sound wave propagation from a point source over a surface with an impedance discontinuity (with B. Enflo), J. of Acoustical Soc. of America, Vol. 82 (1987) 2123-2134
21. Contractive projections onto subsets of L1(0,1), Analysis at Urbana, Vol. I, London Math. Soc. Lecture Note Ser. 137 (1989), 162–184
22. Contractive projections on lp-spaces (with W. J. Davis) London Math.Soc. Lecture Notes Series 137 (1989), 151–161
23. Products of polynomials in many variables (with B. Beauzamy, E. Bombieri and H. Montgomery) J. of Number Theory, Vol. 36 No. 2 (1990) 219-245
24. The largest coefficient in products of polynomials, Functions Spaces , Lecture Notes in Pure and Appl. Math, 136, Edwardsville, II, pp. 97-105
25. Contractive projections onto subsets of Lp-spaces, Lecture Notes in. Pure and Applied Mathematics 136 (1992), 79–94
26. Polynomials in many variables: real vs complex norms (with R. Aron and B. Beauzamy), J. Approx. Theory 74 (1993) 181–198
27. On Sparse Languages L such that LL = Sigma. (with Andrew Granville, Jeffrey Shallit, Sheng Yu ) Discrete Applied Mathematics 52(3) (1994), 275-285
28. Quantitative Estimates for Polynomials in One or Several Variables (with Bernard Beauzamy and Paul Wang) Mathematics Magazine, Vol. 67, No. 4 (Oct., 1994), pp. 243-257
29. Exponential numbers of linear operators in normed spaces, (with V. Gurariy, V.I. Lomonosov, Yu.I. Lyubich), Linear Algebra and its Applications, 219, pp. 225-260 (1995)
30. Some Problems in the Interface between Number Theory, Harmonic Analysis and Geometry of Euclidean Space, Quaestiones Mathematicae 18 (1995), 309-323
31. Stable basis families and complexity lower bounds (with Meera Sitharam) Electronic Colloquium on Computational Complexity (ECCC) 3(49): (1996)
32. Extremal vectors and invariant subspaces (with Shamim Ansari) Trans. Amer. Math. Soc. 350 (1998), 539-558
33. Extremal vectors for a class of linear operators, Functional Analysis and Economic Theory, Springer-Verlag (1998), 61-64
34. Modeling the effects of nutrient concentrations on community production and ecosystem stability: Framework for a Great Lakes Model. (with R.T.Heath, R.Sturtevant and D.Shoup). In Great Lakes Modeling Summit--Focus on Lake Erie. L.Tulen and J.dePinto, Eds., published by Int. Joint Commission, Windsor, ONT., ISBN 1-894280-17-2 (2000), 37-50
35. Some aspects of the Invariant Subspace Problem (with Lomonosov) Handbook of the Geometry of Banach Spaces, Elsevier Science 2001, Vol. 1, Ch. 13, p. 535-559
36. Denseness for norm attaining operator-valued functions (with J. Kover and L. Smithies) Linear Alg. and its Applications, 338 (2001), p. 139-144
37. Harnack's theorem for harmonic compact operator-valued functions (with L. Smithies) Linear Alg. and its Applications, 336 (2001), 21-27
38. A simple reason why Neanderthal ancestry can be consistent with current DNA information (with J. Hawks and M. Wolpoff), Am. J. of Physical Anthropology, Annual Meeting Issue 2001, Supplement 32, page 62.
39. Linability and spaceability of sets in Function Spaces (with V.Gurariy), Proc. Of the Fourth Conference on Function Spaces, AMS (2002-2003)
40. Some results on extremal vectors and invariant subspaces (with Terje Hõim) Proc. Amer. Math. Soc.131 (2003), 379-387
41. A property of strictly singular 1-1 operators (with G. Androulakis)
Ark. Mat. 41, (2003), 233-252
42. Operators with eigenvalues and extreme cases of stability (with Larry Downey) Journal: Proc. Amer. Math. Soc. 132 (2004), 719-724
43. Minimal points and contractive projections. Constructive Theory of Functions, Marin Drinov Publishing House (2006), 98-103
44. An interview with Themistocles M. Rassias ( M.S. Moslehian), Banach J . Math. Anal., 1 (2007), no. 2, 252-260
45. Multiobjective variational programming under generalized (V,ρ)-B-type 1 Functions ( with K.Khazafi and N.Rueda) , Control and Cybernetics no. 3 (2009)
46. Sufficiency and duality for multiobjective control problems under generalized (B, ρ)-type I functions A ( with K.Khazafi and N.Rueda) Journal of Global Optimization Volume 46, Number 1, 111-132, DOI: 10.1007/s10898-009-9412-4 fulltext in ACM DL
47. Extremal vectors and rectifiability (with Aderaw Fenta) Quaestiones Mathematicae - vol 34(1) (2011), 119-123
Lecture at WOTCAM Conference, Richmond, Virginia, 2010
Lecture at YSU, Youngstown, Ohio, 2010
Lectures at Auburn University, Alabama, 2009
Lecture at Tel Aviv University, Israel 2009
Lectures at Tartu University, Estonia, 2008
Lectures at Linkoping University, Linköping, Sweden, 2008
Keynote Speaker at WOTCAM Conference, Richmond, Virginia, 2008
University of Stockholm -Fil.lic. 1967
Topological groups in which multiplication on one side is differentiable or linear.
University of Stockholm - Fil.kand. 1964
Minor: Theoretical Physics
Higher Education Work Experience
University Professor 1989- Present KSU
Visiting Professor 1984-1986 Ohio State University, Columbus, OH
Professor of Applied Mathematics 1983-1990 Royal Institute of Technology, Stockholm
Professor 1978-1983 Institute Mittag-Leffler
Associate Professor 1977-1977 Institute Mittag-Leffler
Directeur de Recherche 1976-1976 Ecole Polytechnique
Sloan Fellow 1975-1977
Associate Professor 1973-1977 Stanford University
Miller Fellow 1971- 1973 University of California Berkeley
Instructor 1970-1971 University of Stockholm
Banach Journal of Mathematics. [2006 - ]
Positivity. [2000 - ]
The Edlund Award - the Swedish Royal Academy of Sciences 1973
Description: - for the solution of ”The Basis Problem”.
Book of the Year - Encyclopedia Britannica 1974
Description: - Report on my solution of ”The Basis Problem” in 1974.
The Celsius medal in gold - the Swedish Royal Society of Science 1977
Description: - for “fundamental contributions to functional analysis".