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Self-adjoint differential vector-operators and matrix Hilbert spaces. I. (English) Zbl 1236.47042
Summary: In the current work, a generalization of the famous Weyl-Kodaira inversion formulas for the case of selfadjoint differential vector operators is proved. A formula for spectral resolutions over an analytical defining set of solutions is discussed. The article is the first part of the planned two-part survey on the structural spectral theory of selfadjoint differential vector operators in matrix Hilbert spaces.
MSC:
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
34L05 General spectral theory of ordinary differential operators
47A10 Spectrum, resolvent
47B25 Linear symmetric and selfadjoint operators (unbounded)
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