An Indefinite Sturm Theory
نویسنده
چکیده
We will use the variational approach to (0.1) as described in [2] and we will stick to the notations of that paper. Given the complex n-dimensional Hermitian space (C, 〈·, ·〉), for any m ∈ N let H m := H(J,C) be the Sobolev space of all H-maps from J := [0, 1] into C. A derivative dependent Hermitian form is the form Ω(x)[u] = Pm i,j=0〈D u(x), ωi,j(x)D u(x)〉, where, each ωi,j is a smooth path of x-dependent Hermitian matrices with constant leading coefficient ωm,m := p2m and such that ωi,2m−1−i = 0 for each i = 0, . . . ,m. Each derivative dependent Hermitian form, defines a Hermitian form q : H m → R by setting q(u) := R
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