## Self-Adjoint Operator Question..

Let be the self-adjoint operator:

$$-a_{0}(x)\frac{d^{2}y}{dx^{2}}+a_{1}(x)y=\lambda_{n}y$$

my question is if we can always choose a0 and a1 in a way that the Eigenvalues are the roots of a given function f(x) with f continous and differentiable... by the existence theorem for differential equations:

$$\frac{d^{2}y}{dx^{2}}=F(x,y)=\frac{-\lambda_{n}y+a_{1}(x)y}{a_{0}(x)}$$

we must have that F and dF/dy must be continuous..so the existence theorem implies that we can always choose a a0 and a1 that satisify that the eigenvalues of the differential equation are the roots of f(x) on condition that a0 and a1 are continous and that a0 has no real roots...is that true?..
 PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity

 Similar discussions for: Self-Adjoint Operator Question.. Thread Forum Replies General Math 3 Linear & Abstract Algebra 8 Calculus & Beyond Homework 14 Introductory Physics Homework 11 General Physics 1