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...
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continued fractions (Liouville numbers). In mathematical physics, Liouville made two fundamental contributions: the Sturm–Liouville theory, which was joint...
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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...
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theory Set theory Shape theory Sheaf theory Singularity theory Soliton theory Spectral theory String theory Sturm-Liouville theory Surgery theory Teichmüller...
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mathematics, physics, engineering, and other disciplines. Sturm–Liouville theory is a theory of a special type of second-order linear ordinary differential...
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basis for principal components analysis and canonical correlation. Sturm–Liouville theory concerns the action of the linear operator L ( y ) = 1 w ( x ) (...
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Set theory — Shape theory — Small cancellation theory — Spectral theory — Stability theory — Stable theory — Sturm–Liouville theory — Surgery theory — Twistor...
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Sturm–Liouville theory, a mathematical theory concerning the solutions of certain differential equations Sturm, Ruger & Co., a firearms manufacturer Sturm series...
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Hilbert space (category Operator theory)
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...
128 KB (17,487 words) - 22:34, 20 June 2024
equation. In his dissertation, Hermann Weyl generalized the classical Sturm–Liouville theory on a finite closed interval to second order differential operators...
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Quantum Liouville equation Sturm–Liouville theory Liouville's theorem (complex analysis) Liouville's theorem (harmonic functions) Liouville's theorem...
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linear differential operator. Lagrange's identity is fundamental in Sturm–Liouville theory. In more than one independent variable, Lagrange's identity is generalized...
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completeness of these solutions is best seen from the viewpoint of Sturm–Liouville theory. We rewrite the differential equation as an eigenvalue problem,...
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general polynomial chaos for uncertainty quantification, and the Sturm-Liouville theory for partial differential equations and fractional calculus. George...
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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...
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(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...
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Paul du Bois-Reymond (section Theory of infinitesimals)
of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational...
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theorem Spectral theory of compact operators Spectral theory of normal C*-algebras Sturm–Liouville theory, Integral equations, Fredholm theory Compact operators...
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problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems, in the linear case, involves...
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\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...
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is a solution. Oscillation theory was initiated by Jacques Charles François Sturm in his investigations of Sturm–Liouville problems from 1836. There he...
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Pi (section Number theory and Riemann zeta function)
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...
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contributions were on abelian groups, graph theory, algebraic numbers, knot theory and Sturm–Liouville theory. In 1915 he began his university studies in...
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Wave equation (section The Sturm–Liouville formulation)
\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...
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Eigenvalues and eigenvectors (category Matrix theory)
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...
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Valentine Atkinson and A. B. Mingarelli, concerns eigenvalues of certain Sturm–Liouville differential operators. In the simplest of formulations let p, q, w...
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(2005) Mathematical Methods for Physicists, 6th edition, chapter 10: Sturm-Liouville Theory — Orthogonal Functions, Academic Press. Price, Justin J. (1975)...
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of elliptic curves Schlesinger's equations Sine-Gordon equation Sturm–Liouville theory of orthogonal polynomials and separable partial differential equations...
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Least-squares spectral analysis Multidimensional transform Spectral theory Sturm–Liouville theory Residue theorem integrals of f(z), singularities, poles But...
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resonance Modal analysis Mode (electromagnetism) Quasinormal mode Sturm–Liouville theory Torsional vibration Vibrations of a circular membrane Blevins, Robert...
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