Selected Papers of Norman Levinson by J.A. NohelSelected Papers of Norman Levinson by J.A. Nohel

Selected Papers of Norman Levinson

EditorJ.A. Nohel, D.H. Sattinger, Gian-Carlo Rota

Hardcover | December 19, 1997

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The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas­ tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami­ cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi­ cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif­ ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.
Title:Selected Papers of Norman LevinsonFormat:HardcoverDimensions:533 pagesPublished:December 19, 1997Publisher:Birkhäuser Boston

The following ISBNs are associated with this title:

ISBN - 10:0817638628

ISBN - 13:9780817638627

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Table of Contents

- Volume 1.- I. Stability and Asymptotic Behavior of Solutions of Ordinary Differential Equations.- Commentary on [L 31] and [L 36].- [L 20] The Growth of the Solutions of a Differential Equation (1941).- [L 24] The Growth of the Solutions of a Differential Equation (1942).- [L 31] The Asymptotic Behavior of a System of Linear Differential Equations (1946).- [L 36] The Asymptotic Nature of Solutions of Linear Systems of Differential Equations (1948).- [L 40] On Stability of Non-Linear Systems of Differential Equations (1949).- [L 68] On u? + (1 + ? g(x)) u = 0 for ?0? | g(x)|dx <_20_3f_20_28_195929_.-20_ii.20_nonlinear20_oscillations20_and20_dynamical20_systems.-20_commentary20_on20_5b_l20_295d_2c_20_5b_l20_385d_20_and20_5b_l20_475d_.-20_5b_l20_235d_20_a20_general20_equation20_for20_relaxation20_oscillations20_28_194229_.-20_5b_l20_255d_20_on20_the20_existence20_of20_periodic20_solutions20_for20_second20_order20_differential20_equations20_with20_a20_forcing20_term20_28_194329_.-20_5b_l20_295d_20_transformation20_theory20_of20_non-linear20_differential20_equations20_of20_the20_second20_order20_28_194429_20_and20_correction20_28_194829_.-20_5b_l20_385d_20_a20_second20_order20_differential20_equation20_with20_singular20_solutions20_28_194929_.-20_5b_l20_475d_20_small20_periodic20_perturbations20_of20_an20_autonomous20_system20_with20_a20_stable20_orbit20_28_195029_.-20_5b_l20_525d_20_forced20_periodic20_solutions20_of20_a20_stable20_non-linear20_system20_of20_differential20_equations20_28_195129_.-20_5b_l20_575d_20_on20_the20_non-uniqueness20_of20_periodic20_solutions20_for20_an20_asymmetric20_lienard20_equation20_28_195229_.-20_iii.20_inverse20_problems20_for20_sturm-liouville20_and20_schrc3b6_dinger20_operators.-20_commentary20_on20_5b_l20_415d_2c_20_5b_l20_435d_20_and20_5b_l20_585d_.-20_5b_l20_415d_20_on20_the20_uniqueness20_of20_the20_potential20_in20_a20_schrc3b6_dinger20_equation20_for20_a20_given20_asymptotic20_phase20_28_194929_.-20_5b_l20_425d_20_determination20_of20_the20_potential20_from20_the20_asymptotic20_phase20_28_194929_.-20_5b_l20_435d_20_the20_inverse20_sturm-liouville20_problem20_28_194929_.-20_5b_l20_585d_20_certain20_explicit20_relationships20_between20_phase20_shift20_and20_scattering20_potential20_28_195329_.-20_iv.20_eigenfunction20_expansions20_and20_spectral20_theory20_for20_ordinary20_differential20_equations.-20_commentary20_on20_5b_l20_495d_2c_20_5b_l20_515d_2c_20_and20_5b_l20_595d_.-20_5b_l20_395d_20_criteria20_for20_the20_limit-point20_case20_for20_second20_order20_linear20_differential20_operators20_28_194929_.-20_5b_l20_495d_20_a20_simplified20_proof20_of20_the20_expansions20_theorem20_for20_singular20_second20_order20_linear20_differential20_equations20_28_195129_.-20_5b_l20_505d_20_addendum20_to20_22_a20_simplified20_proof20_of20_the20_expansions20_theorem20_for20_singular20_second20_order20_linear20_differential20_equations22_20_28_195129_.-20_5b_l20_515d_20_on20_the20_nature20_of20_the20_spectrum20_of20_singular20_second20_order20_linear20_differential20_equations20_28_195129_.-20_5b_l20_535d_20_the20_l-closure20_of20_eigenfunctions20_associated20_with20_selfadjoint20_boundary20_value20_problems20_28_195229_.-20_5b_l20_595d_20_the20_expansion20_theorem20_for20_singular20_self-adjoint20_linear20_differential20_operators20_28_195429_.-20_5b_l20_655d_20_transform20_and20_inverse20_transform20_expansions20_for20_singular20_self-adjoint20_differential20_operators20_28_195829_.-20_v.20_singular20_perturbations20_of20_ordinary20_and20_partial20_differential20_equations.-20_commentary20_on20_5b_l20_455d_2c_20_5b_l20_485d_2c_20_5b_l20_605d_2c_20_5b_l20_625d_2c_20_5b_l20_635d_2c_20_5b_l20_675d_2c_20_5b_l20_565d_20_and20_5b_l20_465d_.-20_5b_l20_455d_20_perturbations20_of20_discontinuous20_solutions20_of20_non-linear20_systems20_of20_differential20_equations20_28_195029_.-20_5b_l20_485d_20_an20_ordinary20_differential20_equation20_with20_an20_interval20_of20_stability2c_20_a20_separation20_point2c_20_and20_an20_interval20_of20_instability20_28_195029_.-20_5b_l20_605d_20_singular20_perturbations20_of20_non-linear20_systems20_of20_differential20_equations20_and20_an20_associated20_boundary20_layer20_equation20_28_195429_.-20_5b_l20_625d_20_periodic20_solutions20_of20_singularly20_perturbed20_systems20_28_195529_.-20_5b_l20_565d_20_a20_boundary20_value20_problem20_for20_a20_nonlinear20_differential20_equation20_with20_a20_small20_parameter20_28_195229_.-20_5b_l20_635d_20_a20_boundary20_value20_problem20_for20_a20_singularly20_perturbed20_differential20_equation20_28_195529_.-20_5b_l20_675d_20_a20_boundary20_value20_problem20_for20_a20_singularly20_perturbed20_differential20_equation20_28_195829_.-20_5b_l20_465d_20_the20_first20_boundary20_value20_problem20_for20_3f_3f_u20_2b_a28_x2c_y29_ux20_2b_20_b28_x2c_y29_uy20_2b_20_c28_x2c_20_y29_u20_3d_20_d28_x2c_y29_20_for20_small20_3f_20_28_195029_.-20_vi.20_elliptic20_partial20_differential20_equations.-20_commentary20_on20_5b_l20_755d_2c_20_5b_l20_785d_2c_20_5b_l875d_.-20_5b_l20_755d_20_positive20_eigenfunctions20_for20_3f_u20_2b_20_3f_f28_u29_20_3d_20_020_28_196229_.-20_5b_l20_785d_20_dirichlet20_problem20_for20_3f_u20_3d_20_f28_p2c_20_u29_20_28_196329_.-20_5b_l20_875d_20_one-sided20_inequalities20_for20_elliptic20_differential20_operators20_28_196529_.-20_vii.20_integral20_equations.-20_commentary20_on20_5b_l20_735d_.-20_5b_l20_325d_20_on20_the20_asymptotic20_shape20_of20_the20_cavity20_behind20_an20_axially20_symmetric20_nose20_moving20_through20_an20_ideal20_fluid20_28_194629_.-20_5b_l20_735d_20_a20_nonlinear20_volterra20_equation20_arising20_in20_the20_theory20_of20_superfluidity20_28_196029_.-20_5b_l20_895d_20_simplified20_treatment20_of20_integrals20_of20_cauchy20_type2c_20_the20_hilbert20_problem20_and20_singular20_integral20_equations.20_appendix3a_20_poincar20_c3a9_-bertrand20_formula20_28_196529_. _28_195929_.-="" ii.="" nonlinear="" oscillations="" and="" dynamical="" systems.-="" commentary="" on="" _5b_l="" _295d_2c_="" _385d_="" _475d_.-="" _235d_="" a="" general="" equation="" for="" relaxation="" _28_194229_.-="" _255d_="" the="" existence="" of="" periodic="" solutions="" second="" order="" differential="" equations="" with="" forcing="" term="" _28_194329_.-="" _295d_="" transformation="" theory="" non-linear="" _28_194429_="" correction="" _28_194829_.-="" singular="" _28_194929_.-="" _475d_="" small="" perturbations="" an="" autonomous="" system="" stable="" orbit="" _28_195029_.-="" _525d_="" forced="" _28_195129_.-="" _575d_="" non-uniqueness="" asymmetric="" lienard="" _28_195229_.-="" iii.="" inverse="" problems="" sturm-liouville="" _schrc3b6_dinger="" operators.-="" _415d_2c_="" _435d_="" _585d_.-="" _415d_="" uniqueness="" potential="" in="" given="" asymptotic="" phase="" _425d_="" determination="" from="" problem="" _585d_="" certain="" explicit="" relationships="" between="" shift="" scattering="" _28_195329_.-="" iv.="" eigenfunction="" expansions="" spectral="" ordinary="" equations.-="" _495d_2c_="" _515d_2c_="" _595d_.-="" _395d_="" criteria="" limit-point="" case="" linear="" operators="" _495d_="" simplified="" proof="" theorem="" _505d_="" addendum="" to="" _22_a="" _equations22_="" _515d_="" nature="" spectrum="" _535d_="" l-closure="" eigenfunctions="" associated="" selfadjoint="" boundary="" value="" _595d_="" expansion="" self-adjoint="" _28_195429_.-="" _655d_="" transform="" _28_195829_.-="" v.="" partial="" _455d_2c_="" _485d_2c_="" _605d_2c_="" _625d_2c_="" _635d_2c_="" _675d_2c_="" _565d_="" _465d_.-="" _455d_="" discontinuous="" systems="" _485d_="" interval="" _stability2c_="" separation="" _point2c_="" instability="" _605d_="" layer="" _625d_="" singularly="" perturbed="" _28_195529_.-="" parameter="" _635d_="" _675d_="" _465d_="" first="" u="" _2b_a28_x2c_y29_ux="" _2b_="" _b28_x2c_y29_uy="" _c28_x2c_="" _y29_u="D(x%2cy)" vi.="" elliptic="" _755d_2c_="" _785d_2c_="" _5b_l875d_.-="" _755d_="" positive="" _28_u29_="0" _28_196229_.-="" _785d_="" dirichlet="" _3d_="" _f28_p2c_="" _u29_="" _28_196329_.-="" _875d_="" one-sided="" inequalities="" _28_196529_.-="" vii.="" integral="" _735d_.-="" _325d_="" shape="" cavity="" behind="" axially="" symmetric="" nose="" moving="" through="" ideal="" fluid="" _28_194629_.-="" _735d_="" volterra="" arising="" superfluidity="" _28_196029_.-="" _895d_="" treatment="" integrals="" cauchy="" _type2c_="" hilbert="" equations.="" _appendix3a_="" poincar="" _c3a9_-bertrand="" formula="">