Within the classical thought of self-adjoint boundary price difficulties for linear usual differential operators there's a primary, yet quite mysterious, interaction among the symmetric (conjugate) bilinear scalar made from the elemental Hilbert house and the skew-symmetric boundary kind of the linked differential expression. This publication offers a brand new conceptual framework, resulting in an efficient dependent strategy, for studying and classifying all such self-adjoint boundary stipulations. this system is conducted by means of introducing leading edge new mathematical constructions which relate the Hilbert house to a fancy symplectic house. This paintings bargains the 1st systematic unique remedy within the literature of those themes: advanced symplectic spaces--their geometry and linear algebra--and quasi-differential operators. gains: Authoritative and systematic exposition of the classical idea for self-adjoint linear traditional differential operators (including a assessment of all appropriate subject matters in texts of Naimark, and Dunford and Schwartz). creation and improvement of recent tools of advanced symplectic linear algebra and geometry and of quasi-differential operators, delivering the single wide remedy of those themes in publication shape. New conceptual and established tools for self-adjoint boundary worth difficulties. vast and exhaustive tabulations of all latest varieties of self-adjoint boundary stipulations for normal and for singular traditional quasi-differential operators of all orders up via six.
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