Displaying similar documents to “The Sturm-Liouville Friedrichs extension”

Minimality of the system of root functions of Sturm-Liouville problems with decreasing affine boundary conditions

Y. N. Aliyev (2007)

Colloquium Mathematicae

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We consider Sturm-Liouville problems with a boundary condition linearly dependent on the eigenparameter. We study the case of decreasing dependence where non-real and multiple eigenvalues are possible. By determining the explicit form of a biorthogonal system, we prove that the system of root (i.e. eigen and associated) functions, with an arbitrary element removed, is a minimal system in L₂(0,1), except for some cases where this system is neither complete nor minimal.

Introduction to Liouville Numbers

Adam Grabowski, Artur Korniłowicz (2017)

Formalized Mathematics

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The article defines Liouville numbers, originally introduced by Joseph Liouville in 1844 [17] as an example of an object which can be approximated “quite closely” by a sequence of rational numbers. A real number x is a Liouville number iff for every positive integer n, there exist integers p and q such that q > 1 and [...] It is easy to show that all Liouville numbers are irrational. Liouville constant, which is also defined formally, is the first transcendental (not algebraic) number....