Polynomial Solutions Linear Differential by Shapiro Boris (10 results)

Buch. Condition: Neu. Neuware -Linear ordinary differential equations with polynomial coefficients and their solutions in the complex plane have been an active area of mathematical research since the mid-19th century, with contributions from such prominent figures as G. Lamé, M. Bôcher, E. Heine, F. Klein, T. Stieltjes, G. D. Birkhoff, and many others. During the 19th century, interest focused mainly on second-order equations because of their importance in physics. The existence of a polynomial solution to a linear differential equation is a very special property, implying in particular the existence of a one-dimensional invariant subspace under the action of the monodromy group on the space of solutions. Polynomial solutions rarely occur for individual linear differential equations, but they typically arise within families of such equations. In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the Bochner-Krall problem in orthogonal polynomials, and the (generalized) Heine-Stieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader.; Seit 1923 erscheinen in der Sammlung Tusculum maßgebende Editionen griechischer und lateinischer Werke mit deutscher Übersetzung. Die Originaltexte werden zudem eingeleitet und umfassend kommentiert; nach der neuen Konzeption bieten schließlich thematische Essays tiefere Einblicke in das Werk, seinen historischen Kontext und sein Nachleben. Die hohe wissenschaftliche Qualität der Ausgaben, gepaart mit dem leserfreundlichen Sprachstil der Einführungs- und Kommentarteile, macht jeden Tusculum-Band zu einer fundamentalen Lektüre nicht nur für Studierende, die sich zum ersten Mal einem antiken Autor nähern, und für Forschende, die spezifische Aspekte eines Werkes vertiefen möchten, sondern für alle, die sich durch vertrauenswürdige Übersetzungen einen Zugang zur Antiken Welt verschaffen wollen. In der Reihe wurden bisher über 340 Titel publiziert, alle erhältlich als Buch und Elektronisches Buch. Dadurch werden bislang vergriffene Titel und Raritäten wieder vollständig verfügbar gemacht. Zusätzlich zu der Buchreihe erscheint bei De Gruyter zum 90-jährigen Jubiläum das Elektronisches Buch-Paket Tusculum Online, eine digitale Sammlung aller von 1923 bis 2013 erschienenen Titel - eine gebührende Würdigung eines wichtigen Stücks deutscher Verlagsgeschichte. 361 pp. Englisch. …

Buch. Condition: Neu. Neuware -Linear ordinary differential equations with polynomial coefficients and their solutions in the complex plane have been an active area of mathematical research since the mid-19th century, with contributions from such prominent figures as G. Lamé, M. Bôcher, E. Heine, F. Klein, T. Stieltjes, G. D. Birkhoff, and many others. During the 19th century, interest focused mainly on second-order equations because of their importance in physics. The existence of a polynomial solution to a linear differential equation is a very special property, implying in particular the existence of a one-dimensional invariant subspace under the action of the monodromy group on the space of solutions. Polynomial solutions rarely occur for individual linear differential equations, but they typically arise within families of such equations. In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the Bochner-Krall problem in orthogonal polynomials, and the (generalized) Heine-Stieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader.; Seit 1923 erscheinen in der Sammlung Tusculum maßgebende Editionen griechischer und lateinischer Werke mit deutscher Übersetzung. Die Originaltexte werden zudem eingeleitet und umfassend kommentiert; nach der neuen Konzeption bieten schließlich thematische Essays tiefere Einblicke in das Werk, seinen historischen Kontext und sein Nachleben. Die hohe wissenschaftliche Qualität der Ausgaben, gepaart mit dem leserfreundlichen Sprachstil der Einführungs- und Kommentarteile, macht jeden Tusculum-Band zu einer fundamentalen Lektüre nicht nur für Studierende, die sich zum ersten Mal einem antiken Autor nähern, und für Forschende, die spezifische Aspekte eines Werkes vertiefen möchten, sondern für alle, die sich durch vertrauenswürdige Übersetzungen einen Zugang zur Antiken Welt verschaffen wollen. In der Reihe wurden bisher über 340 Titel publiziert, alle erhältlich als Buch und Elektronisches Buch. Dadurch werden bislang vergriffene Titel und Raritäten wieder vollständig verfügbar gemacht. Zusätzlich zu der Buchreihe erscheint bei De Gruyter zum 90-jährigen Jubiläum das Elektronisches Buch-Paket Tusculum Online, eine digitale Sammlung aller von 1923 bis 2013 erschienenen Titel - eine gebührende Würdigung eines wichtigen Stücks deutscher Verlagsgeschichte. 361 pp. Englisch. …

Hardcover. Condition: Brand New. 332 pages. 6.69x2.00x9.45 inches. In Stock.

Condition: New. Seit 1923 erscheinen in der Sammlung Tusculum massgebende Editionen griechischer und lateinischer Werke mit deutscher Uebersetzung. Die Originaltexte werden zudem eingeleitet und umfassend kommentiert nach der neuen Konzeption bieten schliesslich .

Buch. Condition: Neu. Polynomial Solutions of Linear Differential Equations | Spectral Problems, Asymptotic and WKB-Analysis | Boris Shapiro | Buch | De Gruyter Expositions in Mathematics | X | Englisch | 2026 | Walter de Gruyter | EAN 9783119147101 | Verantwortliche Person für die EU: Walter de Gruyter GmbH, De Gruyter GmbH, Genthiner Str. 13, 10785 Berlin, productsafety[at]degruyterbrill[dot]com | Anbieter: preigu.…

Buch. Condition: Neu. Neuware - Linear ordinary differential equations with polynomial coefficients and their solutions in the complex plane have been an active area of mathematical research since the mid-19th century, with contributions from such prominent figures as G. Lamé, M. Bôcher, E. Heine, F. Klein, T. Stieltjes, G. D. Birkhoff, and many others. During the 19th century, interest focused mainly on second-order equations because of their importance in physics. The existence of a polynomial solution to a linear differential equation is a very special property, implying in particular the existence of a one-dimensional invariant subspace under the action of the monodromy group on the space of solutions. Polynomial solutions rarely occur for individual linear differential equations, but they typically arise within families of such equations. In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the Bochner-Krall problem in orthogonal polynomials, and the (generalized) Heine-Stieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader.; Seit 1923 erscheinen in der Sammlung Tusculum maßgebende Editionen griechischer und lateinischer Werke mit deutscher Übersetzung. Die Originaltexte werden zudem eingeleitet und umfassend kommentiert; nach der neuen Konzeption bieten schließlich thematische Essays tiefere Einblicke in das Werk, seinen historischen Kontext und sein Nachleben. Die hohe wissenschaftliche Qualität der Ausgaben, gepaart mit dem leserfreundlichen Sprachstil der Einführungs- und Kommentarteile, macht jeden Tusculum-Band zu einer fundamentalen Lektüre nicht nur für Studierende, die sich zum ersten Mal einem antiken Autor nähern, und für Forschende, die spezifische Aspekte eines Werkes vertiefen möchten, sondern für alle, die sich durch vertrauenswürdige Übersetzungen einen Zugang zur Antiken Welt verschaffen wollen. In der Reihe wurden bisher über 340 Titel publiziert, alle erhältlich als Buch und Elektronisches Buch. Dadurch werden bislang vergriffene Titel und Raritäten wieder vollständig verfügbar gemacht. Zusätzlich zu der Buchreihe erscheint bei De Gruyter zum 90-jährigen Jubiläum das Elektronisches Buch-Paket Tusculum Online, eine digitale Sammlung aller von 1923 bis 2013 erschienenen Titel - eine gebührende Würdigung eines wichtigen Stücks deutscher Verlagsgeschichte. …

Buch. Condition: Neu. Neuware -Linear ordinary differential equations with polynomial coefficients and their solutions in the complex plane have been an active area of mathematical research since the mid-19th century, with contributions from such prominent figures as G. Lamé, M. Bôcher, E. Heine, F. Klein, T. Stieltjes, G. D. Birkhoff, and many others. During the 19th century, interest focused mainly on second-order equations because of their importance in physics. The existence of a polynomial solution to a linear differential equation is a very special property, implying in particular the existence of a one-dimensional invariant subspace under the action of the monodromy group on the space of solutions. Polynomial solutions rarely occur for individual linear differential equations, but they typically arise within families of such equations.In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the Bochner-Krall problem in orthogonal polynomials, and the (generalized) Heine-Stieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader.Walter de Gruyter GmbH, Genthiner Straße 13, 10785 Berlin 361 pp. Englisch. …

Hardcover. Condition: new. Hardcover. Linear ordinary differential equations with polynomial coefficients and their solutions in the complex plane have been an active area of mathematical research since the mid-19th century, with contributions from such prominent figures as G. Lame, M. Bocher, E. Heine, F. Klein, T. Stieltjes, G. D. Birkhoff, and many others. During the 19th century, interest focused mainly on second-order equations because of their importance in physics. The existence of a polynomial solution to a linear differential equation is a very special property, implying in particular the existence of a one-dimensional invariant subspace under the action of the monodromy group on the space of solutions. Polynomial solutions rarely occur for individual linear differential equations, but they typically arise within families of such equations. In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the BochnerKrall problem in orthogonal polynomials, and the (generalized) HeineStieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader. The Bibliotheca Teubneriana, established in 1849, has evolved into the world's most venerable and extensive series of editions of Greek and Latin literature, ranging from classical to Neo-Latin texts. Some 4-5 new editions are published every year. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. …

Hardcover. Condition: new. Hardcover. Linear ordinary differential equations with polynomial coefficients and their solutions in the complex plane have been an active area of mathematical research since the mid-19th century, with contributions from such prominent figures as G. Lame, M. Bocher, E. Heine, F. Klein, T. Stieltjes, G. D. Birkhoff, and many others. During the 19th century, interest focused mainly on second-order equations because of their importance in physics. The existence of a polynomial solution to a linear differential equation is a very special property, implying in particular the existence of a one-dimensional invariant subspace under the action of the monodromy group on the space of solutions. Polynomial solutions rarely occur for individual linear differential equations, but they typically arise within families of such equations. In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the BochnerKrall problem in orthogonal polynomials, and the (generalized) HeineStieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader. The Bibliotheca Teubneriana, established in 1849, has evolved into the world's most venerable and extensive series of editions of Greek and Latin literature, ranging from classical to Neo-Latin texts. Some 4-5 new editions are published every year. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. …

Hardcover. Condition: new. Hardcover. Linear ordinary differential equations with polynomial coefficients and their solutions in the complex plane have been an active area of mathematical research since the mid-19th century, with contributions from such prominent figures as G. Lame, M. Bocher, E. Heine, F. Klein, T. Stieltjes, G. D. Birkhoff, and many others. During the 19th century, interest focused mainly on second-order equations because of their importance in physics. The existence of a polynomial solution to a linear differential equation is a very special property, implying in particular the existence of a one-dimensional invariant subspace under the action of the monodromy group on the space of solutions. Polynomial solutions rarely occur for individual linear differential equations, but they typically arise within families of such equations. In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the BochnerKrall problem in orthogonal polynomials, and the (generalized) HeineStieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader. The Bibliotheca Teubneriana, established in 1849, has evolved into the world's most venerable and extensive series of editions of Greek and Latin literature, ranging from classical to Neo-Latin texts. Some 4-5 new editions are published every year. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. …