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Monday, April 13, 2020 | History

1 edition of Sturm-Liouville eigenfunctions expressed in determinant form found in the catalog.

Sturm-Liouville eigenfunctions expressed in determinant form

Michael D. Phillips

# Sturm-Liouville eigenfunctions expressed in determinant form

Published by Naval Postgraduate School, Available from the National Technical Information Service in Monterey, Calif, Springfield, Va .
Written in English

The purpose of this thesis is to investigate and establish Sturm- Liouville properties for special eigenfunctions which are expressed in determinant form. In particular, a special case is presented where the elements of the determinant are Legendre polynomials. This type of determinant has a probability background dealing in birth and death processes. The method of analysis used in this thesis is a new approach to solving this specific example. This investigation involves systems of differential equations and Prufer"s analysis in the phase plane. The following are new results obtained in addition to solving the special case mentioned above. Special determinants of hypergeometric functions also possess Sturm-Liouville properties. As a special case, a different proof of Turan"s Inequality is provided. Finally, several theorems are presented for Sturm-Liouville systems of differential equations with polynomial coefficients.

Edition Notes

The Physical Object ID Numbers Contributions Latta, Gordon, 1923- Pagination 53 p. ; Number of Pages 53 Open Library OL25507818M

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### Sturm-Liouville eigenfunctions expressed in determinant form by Michael D. Phillips Download PDF EPUB FB2

Problems 1–4 of Section are Sturm–Liouville problems. (Problem 5 isn’t, although some authors use a definition of Sturm-Liouville problem that does include it.) We were able to find the eigenvalues of Problems explicitly because in each problem the coefficients in the boundary conditions satisfy $$\alpha\beta=0$$ and \(\rho\delta.

This book, developed from a course taught to senior undergraduates, provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L². Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point Article in Acta Mathematica Scientia 35(3) May.

In mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential his dissertation Hermann Weyl generalized the classical Sturm–Liouville theory on a finite closed interval to second order differential operators with.

Moreover, Proposition showed that any SOLDE can be transformed into a form in which the first-derivative term is absent. By dividing the DE by the coefficient of the second-derivative term if necessary, the study of the most general second-order linear differential operators boils down to that of the so-called Sturm-Liouville (S-L Cited by: 1.

The chapter highlights that the regular Sturm–Liouville equation, written in the form d 2 z/dt 2 − r(t)z + λz = 0 with the boundary conditions z(0) = z(L) = 0 has the asymptotic eigenvalues and eigenfunctions.

It is shown that using the known eigenfunctions and the solutions to an initial value problem, the new first n eigenfunctions and the new potential are found by solving a system of non-singular, linear, algebraic equations.

The new separated, homogeneous boundary conditions and the remaining eigenfunctions are found. 1) then v is an eigenvector of the linear transformation A and the scale factor λ is the eigenvalue corresponding to that eigenvector.

Equation (1) is the eigenvalue equation for the matrix A. Equation (1) can be stated equivalently as (A − λ I) v = 0, {\displaystyle (A-\lambda I)v=0,} (2) where I is the n by n identity matrix and 0 is the zero vector. Eigenvalues and the characteristic. You can write a book review and share your experiences.

Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Since the first volume of this work came out in Germany inthis book, together with its second volume, has remained standard in the field.

Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics.