Equivalence of quotient Hilbert modules
نویسندگان
چکیده
Let M be a Hilbert module of holomorphic functions over a natural function algebra A (Ω), where Ω ⊆Cm is a bounded domain. Let M0 ⊆M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖M0. The invariants are given explicitly in the particular case of k = 2.
منابع مشابه
m at h . FA ] 1 2 O ct 2 00 6 EQUIVALENCE OF QUOTIENT HILBERT MODULES – II RONALD
For any open, connected and bounded set Ω ⊆ C m , let A be a natural function algebra consisting of functions holomorphic on Ω. Let M be a Hilbert module over the algebra A and M0 ⊆ M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module Q = M ⊖ M0 in the case of k = 2...
متن کاملar X iv : m at h / 05 07 55 3 v 1 [ m at h . FA ] 2 7 Ju l 2 00 5 EQUIVALENCE OF QUOTIENT HILBERT MODULES – II RONALD
For any open, connected and bounded set Ω ⊆ C m , let A be a natural function algebra consisting of functions holomorphic on Ω. Let M be a Hilbert module over the algebra A and M0 ⊆ M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module Q = M ⊖ M0 in the case of k = 2...
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