- #1
zetafunction
- 391
- 0
Do Orthogonal Polynomials have always real zeros ??
the idea is , do orthogonal polynomials [tex] p_{n} (x) [/tex] have always REAl zeros ?
for example n=2 there is a second order polynomial with 2 real zeros
if we consider that there is a self-adjoint operator L so [tex] L[p_{n} (x)]= \mu _{n} p_{n} (x) [/tex] if the orthogonal POLYNOMIALS are eigenfunctions of an operator with a real spectrum are ALL the zeros real ? , and if all the zeros are REAL can they be related to the spectrum of L ??
the idea is , do orthogonal polynomials [tex] p_{n} (x) [/tex] have always REAl zeros ?
for example n=2 there is a second order polynomial with 2 real zeros
if we consider that there is a self-adjoint operator L so [tex] L[p_{n} (x)]= \mu _{n} p_{n} (x) [/tex] if the orthogonal POLYNOMIALS are eigenfunctions of an operator with a real spectrum are ALL the zeros real ? , and if all the zeros are REAL can they be related to the spectrum of L ??