Questions tagged [eigenfunctions]

For questions on eigenfunctions, each of a set of independent functions that are the solutions to a given differential equation.

22 questions
120 views

Intuitive understanding of Maximin Principle

From the the book page $324$, does someone could explain to me the Theorem $2$. Maximin principle? I have a bit of difficulties to well understand how works this theorem. A simple example would be ...
925 views

Block diagonalizing two matrices simultaneously

There are two matrices $A$ and $B$ which can not be diagonalized simultaneously. Is it possible to block diagonalize them? What if the matrices have an special pattern? Physics of the problem is that,...
162 views

Eigen values of a Third Order Linear Homogenous ODE

I have two third order linear ODE which have been arrived after applying separation of variables to a system of PDEs \begin{eqnarray} \lambda_h F''' - 2 \lambda_h \beta_h F'' + \left( (\lambda_h \...
79 views

Eigenvalue of a linear transformation substituting $t+1$ for $t$ in polynomials.

Let $V$ be the linear space of all real polynomial $p(x)$ of degree $\leq n$. If $p \in V$, define $q=T(p)$ to mean that $q(t)=p(t+1)$ for all real $t$. Prove that $T$ has only the eigenvalue $1$. ...
660 views

Can we construct Sturm Liouville problems from an orthogonal basis of functions?

Given a sequence of functions orthogonal over some interval, which satisfy Dirichlet boundary conditions at that Interval, can we construct a Sturm Liouville problem that gives these as its ...