# Spaces of D-paraanalytic elements

- Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1990

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topD. Przeworska-Rolewicz. Spaces of D-paraanalytic elements. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1990. <http://eudml.org/doc/268585>.

@book{D1990,

abstract = {Let X be a linear space. Consider a linear equation(*) P(D)x = y, where y ∈ E ⊂ X,with a right invertible operator D ∈ L(X) and, in general, operator coefficients. The main purpose of this paper is to characterize those subspaces E ⊂ X for which all solutions of (*) belong to E (provided that they exist). This leads, even in the classical case of ordinary differential equations with scalar coefficients, to a new class of $C^∞$-functions, which properly contains the classes of analytic functions of a real variable and of functions vanishing together with all derivatives at a point.CONTENTSIntroduction..............................................................................51. Preliminaries........................................................................52. Spaces of smooth elements.................................................83. Spaces of D-analytic elements...........................................214. Spaces of D-paraanalytic elements....................................325. Characterization of .D-paraanalytic elements by means of property (c) and canonical mappings.............396. D-R paraanalytic functions .................................................477. Smooth elements in Leibniz D-algebras..............................598. Weak E-solutions................................................................639. Linear systems with scalar coefficients...............................7910. Linear boundary value problems .....................................82References.............................................................................971985 Mathematics Subject Classification: 47B99, 47E05, 26E20},

author = {D. Przeworska-Rolewicz},

keywords = {right invertible operator; D-paraanalytic element; paraanalytic function; D-analytic element; analytic function; D-R-invariant; R-perfect; D-paraanalyticity; weak E-solvability; boundary value problems},

language = {eng},

location = {Warszawa},

publisher = {Instytut Matematyczny Polskiej Akademi Nauk},

title = {Spaces of D-paraanalytic elements},

url = {http://eudml.org/doc/268585},

year = {1990},

}

TY - BOOK

AU - D. Przeworska-Rolewicz

TI - Spaces of D-paraanalytic elements

PY - 1990

CY - Warszawa

PB - Instytut Matematyczny Polskiej Akademi Nauk

AB - Let X be a linear space. Consider a linear equation(*) P(D)x = y, where y ∈ E ⊂ X,with a right invertible operator D ∈ L(X) and, in general, operator coefficients. The main purpose of this paper is to characterize those subspaces E ⊂ X for which all solutions of (*) belong to E (provided that they exist). This leads, even in the classical case of ordinary differential equations with scalar coefficients, to a new class of $C^∞$-functions, which properly contains the classes of analytic functions of a real variable and of functions vanishing together with all derivatives at a point.CONTENTSIntroduction..............................................................................51. Preliminaries........................................................................52. Spaces of smooth elements.................................................83. Spaces of D-analytic elements...........................................214. Spaces of D-paraanalytic elements....................................325. Characterization of .D-paraanalytic elements by means of property (c) and canonical mappings.............396. D-R paraanalytic functions .................................................477. Smooth elements in Leibniz D-algebras..............................598. Weak E-solutions................................................................639. Linear systems with scalar coefficients...............................7910. Linear boundary value problems .....................................82References.............................................................................971985 Mathematics Subject Classification: 47B99, 47E05, 26E20

LA - eng

KW - right invertible operator; D-paraanalytic element; paraanalytic function; D-analytic element; analytic function; D-R-invariant; R-perfect; D-paraanalyticity; weak E-solvability; boundary value problems

UR - http://eudml.org/doc/268585

ER -

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