associated to each λ. Sturm–Liouville theory is the general study of Sturm–Liouville problems. In particular, for a "regular" Sturm–Liouville problem, it can...

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...

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

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

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

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

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

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...

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

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

linear differential operator. Lagrange's identity is fundamental in Sturm–Liouville theory. In more than one independent variable, Lagrange's identity is generalized...

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

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

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...

(1909), 1–141. Hinton, D. (2005). "Sturm's 1836 Oscillation Results Evolution of the Theory". Sturm-Liouville Theory. pp. 1–27. doi:10.1007/3-7643-7359-8_1...

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

\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...

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

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

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

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...

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

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...

are orthogonal and complete. In general this is guaranteed by Sturm–Liouville theory. Suppose the equation is nonhomogeneous, with the boundary condition...

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

^{2}\,dx\geq 0.\end{aligned}}} Determining boundary conditions in Sturm–Liouville theory Deriving the Euler–Lagrange equation in the calculus of variations...

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

Multidimensional transform Sine and cosine transforms Spectral theory Sturm–Liouville theory Residue theorem integrals of f(z), singularities, poles But...