{\displaystyle \lambda } . Sturm–Liouville theory is the general study of Sturm–Liouville problems. In particular, for a "regular" Sturm–Liouville problem, it can...

continued fractions (Liouville numbers). In mathematical physics, Liouville made two fundamental contributions: the Sturm–Liouville theory, which was joint...

was the co-eponym of the Sturm–Liouville theory with Joseph Liouville. In 1826, with his colleague Jean-Daniel Colladon, Sturm helped make the first experimental...

basis for principal components analysis and canonical correlation. Sturm–Liouville theory concerns the action of the linear operator L ( y ) = 1 w ( x ) (...

mathematics, physics, engineering, and other disciplines. Sturm–Liouville theory is a theory of a special type of second-order linear ordinary differential...

\left((1-x^{2})P_{n}'(x)\right)'+n(n+1)P_{n}(x)=0.} As a consequence of Sturm-Liouville theory, these polynomials are orthogonal eigenfunctions with respect to...

Sturm–Liouville theory, a mathematical theory concerning the solutions of certain differential equations Sturm, Ruger & Co., a firearms manufacturer Sturm series...

Set theory — Shape theory — Small cancellation theory — Spectral theory — Stability theory — Stable theory — Sturm–Liouville theory — Surgery theory — Twistor...

eigenvalues and eigenfunctions of differential equations. For example, the Sturm–Liouville problem arises in the study of the harmonics of waves in a violin string...

theory Spectral theory String theory Sturm-Liouville theory Surgery theory Teichmüller theory Theory of equations Theory of statistics Topos theory Transcendental...

general polynomial chaos for uncertainty quantification, and the Sturm-Liouville theory for partial differential equations and fractional calculus. George...

equation. In his dissertation, Hermann Weyl generalized the classical Sturm–Liouville theory on a finite closed interval to second order differential operators...

problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems, in the linear case, involves...

can include transverse waves that solve the equation central to Sturm–Liouville theory: − d d x [ τ ( x ) d ρ ( x ) d x ] + v ( x ) ρ ( x ) = ω 2 σ ( x...

contributions were on abelian groups, graph theory, algebraic numbers, knot theory and Sturm–Liouville theory. In 1915 he began his university studies in...

\end{aligned}}} This is a special case of the general problem of Sturm–Liouville theory. If a and b are positive, the eigenvalues are all positive, and...

of elliptic curves Schlesinger's equations Sine-Gordon equation Sturm–Liouville theory of orthogonal polynomials and separable partial differential equations...

theorem Spectral theory of compact operators Spectral theory of normal C*-algebras Sturm–Liouville theory, Integral equations, Fredholm theory Compact operators...

Quantum Liouville equation Sturm–Liouville theory Liouville's theorem (complex analysis) Liouville's theorem (harmonic functions) Liouville's theorem...

(2005) Mathematical Methods for Physicists, 6th edition, chapter 10: Sturm-Liouville Theory — Orthogonal Functions, Academic Press. Price, Justin J. (1975)...

basis Spinor spherical harmonics Spin-weighted spherical harmonics Sturm–Liouville theory Table of spherical harmonics Vector spherical harmonics Zernike...

is a solution. Oscillation theory was initiated by Jacques Charles François Sturm in his investigations of Sturm–Liouville problems from 1836. There he...

completeness of these solutions is best seen from the viewpoint of Sturm–Liouville theory. We rewrite the differential equation as an eigenvalue problem,...

of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational...

f(z), singularities, poles Sine and cosine transforms Spectral theory Sturm–Liouville theory Trigonometric moment problem These three did some important...

eigenvalue problems similar to those of Sturm; the discipline that grew out of their work is now called Sturm–Liouville theory. Schwarz studied the first eigenvalue...

operator f ↦ f ″ {\displaystyle f\mapsto f''} , and is constrained by Sturm–Liouville theory to take on only certain specific values. It must be positive, since...

spectral theory differential equations: partial differential equations, separation of variables, ordinary differential equations, Sturm–Liouville theory, eigenfunctions...

analysis, Lagrangian & Hamiltonian mechanics, Laplace transforms, Sturm–Liouville theory, and others) but still can involve mathematical proofs. Engineering...

Valentine Atkinson and A. B. Mingarelli, concerns eigenvalues of certain Sturm–Liouville differential operators. In the simplest of formulations let p, q, w...