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Paper IPM / M / 54

School of Mathematics

Title:

Spectral properties of non-selfadjoint degenerate elliptic ODE's

Author(s):

1.	K. Seddighi
2.	K.Kh. Boimatov

Status:

Published

Journal:

Math. Nachr.

Vol.:

Year:

1995

Pages:

71-79

Supported by:

IPM

Abstract:

In this article we investigate the spectral properties of a non-selfadjoint elliptic operator A on H^l=L² (0,1)^l associated with the noncoercive bilinear form

(1) A [u,v] =

m
∑
i,j=0

⌠
⌡

1

0

< p_i (t) a_ij (t) u⁽ⁱ⁾ (t),

p_j (t)v^(j) (t) > C^l dt,

D[A] =

m
W
2,θ

(0,1)^l,

where θ < m characterizes the order of degeneracy, p_i(t)={t(1−t)}^θ+i−m, a_ij (t) ∈ L^∞ ((0,1);End C^l ) (i,j=0,…, m), u⁽ⁱ⁾ (t) = dⁱ u(t) / dtⁱ.
We consider such questions as the completeness of the system of root vector functions of the operator A in H^l, summability of the Fourier series of elements f ∈ H^l written as a linear combination of root vectors of A by abelian methods with brackets, resolvent estimate of the operator A, description of the domain of the operator A, asymptotic distribution of eigenvalues of the operator A.

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“School of Mathematics”

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