Bio


Osgood is a mathematician by training and applies techniques from analysis and geometry to various engineering problems. He is interested in problems in imaging, pattern recognition, and signal processing.

Academic Appointments


Professional Education


  • PhD, Michigan (1980)

2014-15 Courses


Journal Articles


  • CONCAVE CONFORMAL MAPPINGS AND PRE-VERTICES OF SCHWARZ-CHRISTOFFEL MAPPINGS PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Chuaqui, M., Duren, P., Osgood, B. 2012; 140 (10): 3495-3505
  • Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces IEEE TRANSACTIONS ON INFORMATION THEORY Osgood, B., Siripuram, A., Wu, W. 2012; 58 (7): 4176-4200
  • SCHWARZIAN NORMS AND TWO-POINT DISTORTION PACIFIC JOURNAL OF MATHEMATICS Chuaqui, M., Duren, P., Ma, W., Mejia, D., Minda, D., Osgood, B. 2011; 254 (1): 101-116
  • SCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA Chuaqui, M., Duren, P., Osgood, B. 2011; 36 (2): 449-460
  • Schwarzian Norms and two-point distortion Paci c J. Math Chuaqui, M., Duren, P., Ma, W., Mejía, D., Minda, D., Osgood, B. 2011; 254-1: 101–116
  • On a Theorem of Haimo regarding concave mappings Annales Univ. Marie Curie-Sklodowska, Mathematica Chuaqui, M., Duren, P., Osgood, B. 2011; 65 (2): 17-28
  • Schwarzian derivatives of convex mappings Ann. Acad. Sci. Fenn. Chuaqui, M., Duren, P., Osgood, B. 2011; 36: 449–460
  • Injectivity Criteria for Holomorphic Curves in C-n PURE AND APPLIED MATHEMATICS QUARTERLY Chuaqui, M., Duren, P., Osgood, B. 2011; 7 (1): 223-251
  • OSCILLATION OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY Chuaqui, M., Duren, P., Osgood, B., Stowe, D. 2009; 79 (1): 161-169
  • TWO-POINT DISTORTION THEOREMS FOR HARMONIC MAPPINGS ILLINOIS JOURNAL OF MATHEMATICS Chuaqui, M., Duren, P., Osgood, B. 2009; 53 (4): 1061-1075
  • Falling factorials, generating functions, and conjoint ranking tables Journal of Integer Sequences Osgood, B., Wu, W. 2009; 12
  • Schwarzian derivatives and uniform local univalence Comp. Methods in Function Theory. Chuaqui, M., Duren, P., Osgood, B. 2008; 8 (1): 21–34
  • Schwarzian derivative criteria for valence of analytic and harmonic mappings MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY Chuaqui, M., Duren, P., Osgood, B. 2007; 143: 473-486
  • Univalence criteria for lifts of harmonic mappings to minimal surfaces JOURNAL OF GEOMETRIC ANALYSIS Chuaqui, M., Duren, R., Osgood, B. 2007; 17 (1): 49-74
  • A generalization of Nehari's p-criterion for univalence Complex Variables and Elliptic Equations Chuaqui, M., Osgood, B. 2007; 52: 225– 233
  • Ellipses, near ellipses, and harmonic Mobius transformations PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Chuaqui, M., Duren, P., Osgood, B. 2005; 133 (9): 2705-2710
  • Optimal variable-density K-SPACE sampling in MRI 2004 2ND IEEE INTERNATIONAL SYMPOSIUM ON BIOMEDICAL IMAGING: MACRO TO NANO, VOLS 1 AND 2 Lee, J. H., Osgood, B., Nishimura, D. G. 2004: 237-240
  • Curvature properties of planar harmonic mappings Comp. Methods in Function Theory Chuaqui, M., Duren, P., Osgood, B. 2004; 4: 127– 142
  • The Schwarzian derivative for harmonic mappings JOURNAL D ANALYSE MATHEMATIQUE Chuaqui, M., Duren, P., Osgood, B. 2003; 91: 329-351
  • Recent progress on the geometry of univalence criteria Cont. Math. vol. Chuaqui, M., Osgood, B. 1999; 240: 75– 87
  • The Schwarzian derivative, conformal connections, and Mobius structures JOURNAL D ANALYSE MATHEMATIQUE Osgood, B., Stowe, D. 1998; 76: 163-190
  • Coefficients of small univalent functions Results in Mathematics Chuaqui, M., Osgood, B., Pommerenke, Ch. 1998; 33: 79–86
  • John domains and a univalence criterion of Ahlfors Results in Mathematics Chuaqui, M., Osgood, B. 1998; 33: 203–207
  • Old and new on the Schwarzian derivative QUASICONFORMAL MAPPINGS AND ANALYSIS Osgood, B. 1998: 275-308
  • Finding complete conformal metrics to extend conformal mappings INDIANA UNIVERSITY MATHEMATICS JOURNAL Chuaqui, M., Osgood, B. 1998; 47 (4): 1273-1291
  • General univalence criteria in the disk: Extensions and extremal function ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA Chuaqui, M., Osgood, B. 1998; 23 (1): 101-132
  • Functions with prescribed quasisymmetry quotients PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Chuaqui, M., Osgood, B., Stowe, D. 1997; 125 (7): 2195-2197
  • Weak Schwarzians, bounded hyperbolic distortion, and smooth quasisymmetric functions JOURNAL D ANALYSE MATHEMATIQUE Chuaqui, M., Osgood, B. 1996; 68: 209-252
  • John domains, quasidisks, and the Nehari class JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Chuaqui, M., Osgood, B., POMMERENKE, C. 1996; 471: 77-114
  • AN EXTENSION OF A THEOREM OF GEHRING AND POMMERENKE ISRAEL JOURNAL OF MATHEMATICS Chuaqui, M., Osgood, B. 1995; 91 (1-3): 393-407
  • AHLFORS-WEILL EXTENSIONS OF CONFORMAL-MAPPINGS AND CRITICAL-POINTS OF THE POINCARE METRIC COMMENTARII MATHEMATICI HELVETICI Chuaqui, M., Osgood, B. 1994; 69 (4): 659-668
  • SHARP DISTORTION-THEOREMS ASSOCIATED WITH THE SCHWARZIAN DERIVATIVE JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES Chuaqui, M., Osgood, B. 1993; 48: 289-298
  • THE SCHWARZIAN DERIVATIVE AND CONFORMAL MAPPING OF RIEMANNIAN-MANIFOLDS DUKE MATHEMATICAL JOURNAL Osgood, B., Stowe, D. 1992; 67 (1): 57-99
  • THE SCHWARZIAN DERIVATIVE AND CONFORMALLY NATURAL QUASI-CONFORMAL EXTENSIONS FROM ONE-DIMENSION TO 2-DIMENSION TO 3-DIMENSIONS MATHEMATISCHE ANNALEN Chuaqui, M., Osgood, B. 1992; 292 (2): 267-280
  • The Möbius connection in the bundle of conformal 2-jets Idaho State Conf. on Vector Bundles in Complex Di . Geom. Osgood, B. 1992
  • A GENERALIZATION OF NEHARIS UNIVALENCE CRITERION COMMENTARII MATHEMATICI HELVETICI Osgood, B., Stowe, D. 1990; 65 (2): 234-242
  • MODULI SPACE, HEIGHTS AND ISOSPECTRAL SETS OF PLANE DOMAINS ANNALS OF MATHEMATICS Osgood, B., Phillips, R., Sarnak, P. 1989; 129 (2): 293-362
  • EXTREMALS OF DETERMINANTS OF LAPLACIANS JOURNAL OF FUNCTIONAL ANALYSIS Osgood, B., Phillips, R., Sarnak, P. 1988; 80 (1): 148-211
  • COMPACT ISOSPECTRAL SETS OF SURFACES JOURNAL OF FUNCTIONAL ANALYSIS Osgood, B., Phillips, R., Sarnak, P. 1988; 80 (1): 212-234
  • COMPACT ISOSPECTRAL SETS OF PLANE DOMAINS PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Osgood, B., Phillips, R., Sarnak, P. 1988; 85 (15): 5359-5361

    Abstract

    Any isospectral family of two-dimensional Euclidean domains is shown to be compact in the C(infinity) topology. Previously Melrose, using heat invariants, was able to establish the C(infinity) compactness of the curvature of the boundary curves. The additional ingredient used in this paper to obtain the compactness of the domains is the behavior of the determinant of the Laplacian near the boundary of the moduli space.

    View details for Web of Science ID A1988P574600004

    View details for PubMedID 16593960

  • THE SCHWARZIAN DISTANCE BETWEEN DOMAINS - A QUESTION ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA Osgood, B., Stowe, D. 1987; 12 (2): 313-318
  • The quasihyperbolic metric and associated estimates on the hyperbolic metric Jour. d'Analyse Math. Martin, G., Osgood, B. 1986; 47: 37–53
  • Hyperbolic curvature and conformal mapping Bull. London Math. Soc. Flinn, B., Osgood, B. 1986; 18: 272–276
  • Some properties of f"/f' and the Poincaré metric Indiana Univ. Math. Jour. Osgood, B. 1982; 31: 449–461
  • Univalence criteria in multiply connected domains Trans. Amer. Math. Soc. Osgood, B. 1980; 260: 459–473

Books and Book Chapters


  • Applied Calculus Osgood, B., Gleason, A., Hallett, D. H. John Wiley & Sons, New York. 2006
  • Calculus Osgood, B., Gleason, A., Hallett, D. H. John Wiley & Sons, New York. 2005
  • Single and Multivariable Calculus Osgood, B., Gleason, A., Hallett, D. H. John Wiley & Sons, New York. 2005
  • Multivariable Calculus Osgood, B., Gleason, A., Hallett, D. H. John Wiley & Sons, New York. 2005
  • Quasiconformal mappings and analysis: A collection of papers honoring F. W. Gehring Papers from the International Symposium held in Ann Arbor, MI, August 1995. Osgood, B. edited by Duren, P., Heinonen, J., Osgood, B. Springer-Verlag, New York. 1998

Conference Proceedings


  • Ellipses, near ellipses, and harmonic Möbius transformations Chuaqui, M., Duren, P., Osgood, B. 2005