Len Bos

Professor Emeritus

Department of Mathematics and Statistics

PhD

University of Toronto, 1981

MSc

University of Toronto, 1977

BSc

University of Toronto, 1976

Contact information


Research and teaching

Research interests

  • Markovs inequality on sets with cusps and its relation to other phenomenon such as Sobolev-type inequalities and the extension of C (infinity) functions
  • Tangential Markov/Bernstein inequalities on manifolds
  • Weighted splines and minimum norm networks

Publications

Book

  • Bos, Len and Waldron, Shayne. On the structure of {K}ergin interpolation for points in general position 137. Birkh\"auser, 2001. 75-87. Print.
  • Bos, Len and Maier, Ulrike. On the asymptotics of points which maximize determinants of the form {$\det[g(\vert x\sb i-x\sb j\vert )]$} 107. Wiley-VCH, Berlin, 1999. 107-128. Print.
  • Bos, Len and Pavlov, Boris. Absolute continuity of convolutions of singular measures and new branches of spectrum of {L}iouvillians and few-body {H}amiltonians 399. Chapman \& Hall/CRC, Boca Raton, FL, 1999. 308-322. Print.
  • Bos, Len and Holland, Darius. Radial extensions of vertex data 18. Amer. Math. Soc., 1999. 5-14. Print.
  • Bos, Len, Levenberg, N. and Taylor, B. A.. Characterization of smooth, compact algebraic curves in {${\bf R}\sp 2$} 31. Polish Acad. Sci., 1995. 125-134. Print.
  • Bos, Len and Milman, P. D.. On {M}arkov and {S}obolev type inequalities on sets in {$\bold R\sp n$} World Sci. Publishing, 1993. 81-100. Print.
  • Bos, Len and Milman, P. D.. The equivalence of the usual and quotient topologies for {$C\sp \infty(E)$} when {$E\subset{\bf R}\sp n$} is {W}hitney {$p$}-regular 356. Kluwer Acad. Publ., 1992. 279-292. Print.
  • Bos, Len and Salkauskas, Kes. Weighted splines based on piecewise polynomial weight functions , SIAM, 1992. 87-98. Print.
  • Bos, Len, Grabenstetter, J. E. and Salkauskas, Kes. Finite element interpolation with weighted smoothing 2. Acad. Cienc. Exact. F\'\i s. Qu\'\i m. Nat. Zaragoza, 1990. 17-23. Print.
  • Bos, Len. Asymptotics for the {C}hristoffel function for the equilibrium measure on a ball in {${\bf R}\sp m$} Academic Press, 1989. 97-100. Print.
  • Bos, Len and Gotay, Mark J.. Reduced canonical formalism for a particle with zero angular momentum World Sci. Publishing, 1984. 83-91. Print.
  • Bos, Len and Bloom, Thomas. On the convergence of {K}ergin interpolants of analytic functions Academic Press, 1983. 369-374. Print.

Journal article

  • Brudnyi, Alex, Bos, Len and Levenberg, Norm. "On polynomial inequalities on exponential curves in C^n". Constr. Approx. 31.1 (2010): 139-147. Print.
  • Bos, Len, Brudnyi, Alex, Levenberg, N. and Totik, V.. "Tangential Markov inequalities on transcendental curves". Constructive Approximation. An International Journal for Approximations and Expansions 19.3 (2003): 339-354. Print.
  • Bos, Len and Maier, U.. "On the asymptotics of {F}ekete-type points for univariate radial basis interpolation". Journal of Approximation Theory 119.2 (2002): 252-270. Print.
  • Bos, Len, Ware, Antony and Pavlov, B. S.. "On a semi-spectral method for pricing an option on a mean-reverting asset". Quantitative Finance 2.5 (2002): 337-345. Print.
  • Bagby, T., Bos, Len and Levenberg, N.. "Multivariate simultaneous approximation". Constructive Approximation. An International Journal for Approximations and Expansions 18.4 (2002): 569-577. Print.
  • Bos, Len and Marchi, Stefano. "On the limit under scaling of polynomial {L}agrange interpolation on analytic manifolds". Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento, 68, part I (2002): 303-314. Print.
  • Bos, Len, Calvi, Jean and Levenberg, Norman. "On the {S}iciak extremal function for real compact convex sets". Arkiv f\"or Matematik 39.2 (2001): 245-262. Print.
  • Bos, Len, Taylor, M. A. and Wingate, B. A.. "Tensor product {G}auss-{L}obatto points are {F}ekete points for the cube". Mathematics of Computation 70.236 (2001): 1543-1547 (electronic). Print.
  • Bos, Len and Marchi, Stefano. "Fekete points for bivariate polynomials restricted to {$y=x\sp m$}". East Journal on Approximations 6.2 (2000): 189-200. Print.
  • Bos, Len and Marchi, S.. "Limiting values under scaling of the {L}ebesgue function for polynomial interpolation on spheres". Journal of Approximation Theory 96.2 (1999): 366-377. Print.
  • Korevaar, J. and Bos, Len. "Characterization of algebraic curves by {C}hebyshev quadrature". Journal d'Analyse Math\'ematique 75. (1998): 233-246. Print.
  • Bos, Len, Levenberg, N., Milman, P. D. and Taylor, B. A.. "Tangential {M}arkov inequalities on real algebraic varieties". Indiana University Mathematics Journal 47.4 (1998): 1257-1272. Print.
  • Bos, Len, Vecchia, B. and Mastroianni, G.. "On the asymptotics of {C}hristoffel functions for centrally symmetric weight functions on the ball in {$\bold R\sp d$}". Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento, 52, Vol. I (1998): 277-290. Print.
  • Bos, Len and Calvi, Jean. "Kergin interpolants at the roots of unity approximate {$C\sp 2$} functions". Journal d'Analyse Math\'ematique 72. (1997): 203-221. Print.
  • Bos, Len and Holland, Darius. "Network splines". Results in Mathematics. Resultate der Mathematik 30.3-4 (1996): 228-258. Print.
  • Bagby, Thomas, Bos, Len and Levenberg, Norman. "Quantitative approximation theorems for elliptic operators". Journal of Approximation Theory 85.1 (1996): 69-87. Print.
  • Bos, Len, Grabenstetter, J. E. and Salkauskas, Kes. "Pseudo-tensor product interpolation and blending with families of univariate schemes". Computer Aided Geometric Design 13.5 (1996): 429-440. Print.
  • Bos, Len, Levenberg, N., Milman, P. and Taylor, B. A.. "Tangential {M}arkov inequalities characterize algebraic submanifolds of {${\bf R}\sp N$}". Indiana University Mathematics Journal 44.1 (1995): 115-138. Print.
  • Bos, Len and Milman, P. D.. "Sobolev-{G}agliardo-{N}irenberg and {M}arkov type inequalities on subanalytic domains". Geometric and Functional Analysis 5.6 (1995): 853-923. Print.
  • Bos, Len. "Asymptotics for the {C}hristoffel function for {J}acobi like weights on a ball in {${\bf R}\sp m$}". New Zealand Journal of Mathematics 23.2 (1994): 99-109. Print.
  • Bos, Len and Salkauskas, Kes. "Limits of weighted splines based on piecewise constant weight functions". The Rocky Mountain Journal of Mathematics 23.2 (1993): 483-493. Print.
  • Bloom, T., Bos, Len, Christensen, C. and Levenberg, N.. "Polynomial interpolation of holomorphic functions in {${\bf C}$} and {${\bf C}\sp n$}". The Rocky Mountain Journal of Mathematics 22.2 (1992): 441-470. Print.
  • Salkauskas, Kes and Bos, Len. "Weighted splines as optimal interpolants". The Rocky Mountain Journal of Mathematics 22.2 (1992): 705-717. Print.
  • Bos, Len. "On certain configurations of points in {${\bf R}\sp n$} which are unisolvent for polynomial interpolation". Journal of Approximation Theory 64.3 (1991): 271-280. Print.
  • Bos, Len. "Some remarks on the {F}ej\'er problem for {L}agrange interpolation in several variables". Journal of Approximation Theory 60.2 (1990): 133-140. Print.
  • Bos, Len. "A characteristic of points in {${\bf R}\sp 2$} having {L}ebesgue function of polynomial growth". Journal of Approximation Theory 56.3 (1989): 316-329. Print.
  • Bos, Len and Salkauskas, Kes. "Moving least-squares are {B}ackus-{G}ilbert optimal". Journal of Approximation Theory 59.3 (1989): 267-275. Print.
  • Bos, Len and Salkauskas, Kes. "Comment on the representation of splines as {B}oolean sums". Journal of Approximation Theory 53.2 (1988): 155-162. Print.
  • Bos, Len and Salkauskas, Kes. "On the matrix {$[\vert x\sb i-x\sb j\vert \sp 3]$} and the cubic spline continuity equations". Journal of Approximation Theory 51.1 (1987): 81-88. Print.
  • Gotay, Mark J. and Bos, Len. "Singular angular momentum mappings". Journal of Differential Geometry 24.2 (1986): 181-203. Print.
  • Bos, Len and Torrence, R. J.. "Comment on the {L}iouville equation and multisolitons". Physics Letters. A 111.3 (1985): 95-96. Print.
  • Bos, Len. "Bounding the {L}ebesgue function for {L}agrange interpolation in a simplex". Journal of Approximation Theory 38.1 (1983): 43-59. Print.
  • Bos, Len. "On {K}ergin interpolation in the disk". Journal of Approximation Theory 37.3 (1983): 251-261. Print.
  • Galler, Bruce I. and Bos, Len. "A model of transaction blocking in databases". Performance Evaluation. An International Journal 3.2 (1983): 95-122. Print.