Per Enflo Math or Music?- Yes, Math AND Music!

Per Enflo ■ Publications ■ CV

Publications

Web Publications

A simple reason, why Neandertal ancestry can be consistent with current DNA information >>

Reproduction strategy as a driving force for Human Evolution >>

"Neanderthals are not counted out. New torch giving fuel to the debate on the origin of man" >>

Book Chapters

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

Journal Articles

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

(1972), 281-288

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, Function 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

48. Some results and open questions on spaceability in function spaces. (with V. Gurariy and J. Seoane-Sepúlveda) Transactions of the American Mathematical Society. 366 (2014), 611-625 >>pdf

49. On Montgomery's conjecture and the distribution of Dirichlet sums, (with V. Gurariy and J. Seoane-Sepúlveda), Journal of Functional Analysis 267, (2014) 1241-1255 pdf >>

50. Reproductively disadvantageous regions and archaic humans (with Gustavo A. Muñoz-Fernández, Juan B. Seoane-Sepúlveda) arXiv.org Submitted on 23 May 2017,

https://arxiv.org/abs/1705.0821

51. Quantitative and qualitative estimates on the norm of products of polynomials, (with G. Araújo, G.A. Muñoz-Fernández, et al.) Israel J. Math. 236, (2020) 727–745 link>

52. A history of solving some famous problems in mathematical analysis, P H Enflo, M S Moslehian & J B Seoane-Sepúlveda (2022) British Journal for the History of Mathematics, 37:1, 64-80, DOI:10.1080/26375451.2022.2037358

53. On the invariant subspace problem in Hilbert spaces. [In this paper we show that every bounded linear operator T on a Hilbert space H has a closed non-trivial invariant subspace.] Submitted 24 May, 2023; originally announced May 2023. Comments:13 pages MSC Class:47A15; 47B02. Available online >> arXiv:2305.15442

Education

University of Stockholm

- Filosofiska Graden 1970

Major: Mathematics

Investigations on Hilbert's fifth problem for non locally compact groups. Dissertation, Stockholm University, 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

University of Stockholm -Fil.lic. 1967

Major: Mathematics

Topological groups in which multiplication on one side is differentiable or linear.

University of Stockholm - Fil.kand. 1964

Major: Mathematics

Minor: Theoretical Physics

Positions held

University Professor 1989- 2012, Kent State University, OH

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

Editor

Banach Journal of Mathematics. [2006 - 2023]

Positivity. [2000 - ]

Awards

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).

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".

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”.

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