1. Georgian Technical University
N. Chachava, I. Lomidze
SYMBOLIC ESTIMATION OF DISTANCES BETWEEN EIGENVALUES OF HERMITIAN OPERATOR
SCCTW’2016
Tbilisi,

2. Real roots only. 1)
Roots have multiplicities
We can express
with any precision by
coefficients If
then there is one root If
then there is no roots inside If
(or ),
(or )
is a root and
neighbor cells are empty.

3. Minimal polynomial, which has only simple roots ( )2)
Minimal polynomial, which has only simple roots ( )
where
All parameteres can be rationally expressed by
I. Lomidze. Criteria of Unitary Equivalence of Hermitian Operators with Degenerate Spectrum. Georgian Math. Journal. http// v.3, #2, 1996, p

4. 3)
As we have used only symmetric functions
all our results (may be, except the limits and ) can be expressed (rationally) by the coefficients of the minimal polynomial which form a basis in the space of symmetric functions. These coefficients, in theirs turn, can be rationally expressed by the coefficients of the given polynomial

5. 4)
For

6. 5)
For
For

7. 6)
Number of steps needed to find if
where
(for any and ), If
then

8. 7)
Number of steps needed to find (or )
(or ):
where If
then

9. Thank you
for attention