Verfügbarkeit: Methods of modern mathematical physics

Methods of modern mathematical physics: 1 Functional analysis

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Bibliographische Detailangaben
Beteiligte Personen:	Reed, Michael 1942- (VerfasserIn), Simon, Barry 1946- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Acad. Press 1980
Ausgabe:	Rev. and enl. ed.
Schlagwörter:	Mathematische Physik Mathematical physics Funktionalanalysis
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001543931&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 400 S. graph. Darst.
ISBN:	0125850506 9780125850506

Internformat

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Datensatz im Suchindex

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adam_text	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author	Reed, Michael 1942- Simon, Barry 1946-
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discipline	Physik Mathematik
edition	Rev. and enl. ed.
format	Book
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isbn	0125850506 9780125850506
language	English
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oclc_num	264141771
open_access_boolean
owner	DE-91G DE-BY-TUM DE-384 DE-703 DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-862 DE-BY-FWS DE-739 DE-29T DE-92 DE-634 DE-83 DE-188 DE-11 DE-573
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physical	XV, 400 S. graph. Darst.
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spellingShingle	Reed, Michael 1942- Simon, Barry 1946- Methods of modern mathematical physics Mathematische Physik Mathematical physics Funktionalanalysis (DE-588)4018916-8 gnd
subject_GND	(DE-588)4018916-8
title	Methods of modern mathematical physics
title_auth	Methods of modern mathematical physics
title_exact_search	Methods of modern mathematical physics
title_full	Methods of modern mathematical physics 1 Functional analysis Michael Reed ; Barry Simon
title_fullStr	Methods of modern mathematical physics 1 Functional analysis Michael Reed ; Barry Simon
title_full_unstemmed	Methods of modern mathematical physics 1 Functional analysis Michael Reed ; Barry Simon
title_short	Methods of modern mathematical physics
title_sort	methods of modern mathematical physics functional analysis
topic	Mathematische Physik Mathematical physics Funktionalanalysis (DE-588)4018916-8 gnd
topic_facet	Mathematische Physik Mathematical physics Funktionalanalysis
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001543931&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV002367875
work_keys_str_mv	AT reedmichael methodsofmodernmathematicalphysics1 AT simonbarry methodsofmodernmathematicalphysics1

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