000			03779nam a22004455i 4500
001			978-0-387-84895-2
003			DE-He213
005			20251006084424.0
007			cr nn 008mamaa
008			100301s2009 xxu| s |||| 0|eng d
020			_a9780387848952
020			_a99780387848952
024	7		_a10.1007/978-0-387-84895-2 _2doi
082	0	4	_a515.7 _223
100	1		_aGrubb, Gerd. _eauthor.
245	1	0	_aDistributions and Operators _h[electronic resource] / _cby Gerd Grubb.
264		1	_aNew York, NY : _bSpringer New York, _c2009.
300			_aXII, 464 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v252
505	0		_aDistributions and derivatives -- Motivation and overview -- Function spaces and approximation -- Distributions. Examples and rules of calculus -- Extensions and applications -- Realizations and Sobolev spaces -- Fourier transformation of distributions -- Applications to differential operators. The Sobolev theorem -- Pseudodifferential operators -- Pseudodifferential operators on open sets -- Pseudodifferential operators on manifolds, index of elliptic operators -- Boundary value problems -- Boundary value problems in a constant-coefficient case -- Pseudodifferential boundary operators -- Pseudodifferential methods for boundary value problems -- Topics on Hilbert space operators -- Unbounded linear operators -- Families of extensions -- Semigroups of operators.
520			_aThis book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. Additionally, the aim is to show how the theory is combined with the study of operators in Hilbert space by methods of functional analysis, with applications to partial and ordinary differential equations. Here, the author provides an introduction to unbounded operators in Hilbert space, including a complete theory of extensions of operators, and applications using contraction semigroups. In more advanced parts of the book, the author shows how distribution theory is used to define pseudodifferential operators on manifolds, and gives a detailed introduction to the pseudodifferential boundary operator calculus initiated by Boutet de Monvel, which allows a modern treatment of elliptic boundary value problems. This book is aimed at graduate students, as well as researchers interested in its special topics, and as such, the author provides careful explanations along with complete proofs, and a bibliography of relevant books and papers. Each chapter has been enhanced with many exercises and examples. Unique topics include: * the interplay between distribution theory and concrete operators; * families of extensions of nonselfadjoint operators; * an illustration of the solution maps between distribution spaces by a fully worked out constant-coefficient case; * the pseudodifferential boundary operator calculus; * the Calderón projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen.
650		0	_aMATHEMATICS.
650		0	_aFUNCTIONAL ANALYSIS.
650		0	_aDIFFERENTIAL EQUATIONS, PARTIAL.
650	1	4	_aMATHEMATICS.
650	2	4	_aFUNCTIONAL ANALYSIS.
650	2	4	_aPARTIAL DIFFERENTIAL EQUATIONS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387848945
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v252
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-84895-2 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59243 _d59243