1050:
22:
308:
506:
372:
939:
602:
223:
765:
892:
747:
723:
615:
704:
595:
974:
619:
770:
826:
425:
1053:
775:
760:
588:
325:
790:
1035:
795:
989:
913:
1030:
846:
780:
882:
683:
755:
1079:
979:
1074:
1010:
954:
918:
384:
89:. One of their main advantages is that they offer a way to deal with the fact that the Sobolev space
993:
959:
897:
611:
129:
984:
851:
413:
380:
191:
86:
964:
560:
969:
887:
856:
836:
821:
816:
811:
648:
550:
572:
831:
785:
733:
728:
699:
580:
569:
519:
184:
125:
94:
658:
1020:
872:
673:
303:{\displaystyle \lim _{k\to \infty }u_{k}=u{\mbox{ in }}L^{1}(\Omega ;\mathbf {R} ^{m})}
76:
1068:
1025:
949:
678:
663:
653:
187:
102:
83:
1015:
668:
638:
409:
144:
80:
47:
944:
934:
841:
643:
117:
105:
68:
877:
717:
713:
709:
564:
555:
534:
36:
163:
32:
101:
is not reflexive, it is not always true that a bounded sequence has a
584:
15:
43:
539:-th derivatives are measures defined on Ω̅"
260:
428:
328:
226:
1003:
927:
906:
865:
804:
746:
692:
627:
501:{\displaystyle \|(u,v)\|:=\|u\|_{L^{1}}+\|v\|_{M},}
940:Spectral theory of ordinary differential equations
500:
367:{\displaystyle \lim _{k\to \infty }\nabla u_{k}=v}
366:
302:
390:regular Borel measures on the closure of Ω.
330:
228:
108:, which is a desideratum in many applications.
596:
535:"Spaces of functions on domain Ω, whose
8:
486:
479:
460:
453:
447:
429:
631:
603:
589:
581:
554:
489:
468:
463:
427:
352:
333:
327:
291:
286:
270:
259:
247:
231:
225:
893:Group algebra of a locally compact group
197:there exists a sequence of functions
7:
143:) is defined to be the space of all
345:
340:
279:
238:
14:
1049:
1048:
975:Topological quantum field theory
287:
20:
179:(thought of as the gradient of
444:
432:
337:
297:
276:
235:
35:format but may read better as
1:
771:Uniform boundedness principle
522:norms of the two components.
1096:
914:Invariant subspace problem
1044:
634:
883:Spectrum of a C*-algebra
556:10.21136/CPM.1972.117746
980:Noncommutative geometry
412:when equipped with the
75:are generalizations of
44:converting this article
1036:Tomita–Takesaki theory
1011:Approximation property
955:Calculus of variations
502:
368:
304:
1031:Banach–Mazur distance
994:Generalized functions
533:Souček, Jiří (1972).
503:
369:
305:
206:in the Sobolev space
776:Kakutani fixed-point
761:Riesz representation
514:i.e. the sum of the
426:
383:in the space of all
326:
224:
960:Functional calculus
919:Mahler's conjecture
898:Von Neumann algebra
612:Functional analysis
985:Riemann hypothesis
684:Topological vector
498:
364:
344:
300:
264:
242:
79:, named after the
46:, if appropriate.
1062:
1061:
965:Integral operator
742:
741:
543:Časopis Pěst. Mat
400:The Souček space
329:
263:
227:
103:weakly convergent
65:
64:
1087:
1052:
1051:
970:Jones polynomial
888:Operator algebra
632:
605:
598:
591:
582:
568:
558:
507:
505:
504:
499:
494:
493:
475:
474:
473:
472:
373:
371:
370:
365:
357:
356:
343:
309:
307:
306:
301:
296:
295:
290:
275:
274:
265:
261:
252:
251:
241:
116:Let Ω be a
60:
57:
51:
42:You can help by
24:
23:
16:
1095:
1094:
1090:
1089:
1088:
1086:
1085:
1084:
1065:
1064:
1063:
1058:
1040:
1004:Advanced topics
999:
923:
902:
861:
827:Hilbert–Schmidt
800:
791:Gelfand–Naimark
738:
688:
623:
609:
578:
532:
529:
520:total variation
485:
464:
459:
424:
423:
397:
348:
324:
323:
285:
266:
243:
222:
221:
205:
126:Euclidean space
114:
95:reflexive space
61:
55:
52:
41:
25:
21:
12:
11:
5:
1093:
1091:
1083:
1082:
1080:Sobolev spaces
1077:
1067:
1066:
1060:
1059:
1057:
1056:
1045:
1042:
1041:
1039:
1038:
1033:
1028:
1023:
1021:Choquet theory
1018:
1013:
1007:
1005:
1001:
1000:
998:
997:
987:
982:
977:
972:
967:
962:
957:
952:
947:
942:
937:
931:
929:
925:
924:
922:
921:
916:
910:
908:
904:
903:
901:
900:
895:
890:
885:
880:
875:
873:Banach algebra
869:
867:
863:
862:
860:
859:
854:
849:
844:
839:
834:
829:
824:
819:
814:
808:
806:
802:
801:
799:
798:
796:Banach–Alaoglu
793:
788:
783:
778:
773:
768:
763:
758:
752:
750:
744:
743:
740:
739:
737:
736:
731:
726:
724:Locally convex
721:
707:
702:
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690:
689:
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681:
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651:
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635:
629:
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528:
525:
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523:
511:
510:
509:
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497:
492:
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484:
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471:
467:
462:
458:
455:
452:
449:
446:
443:
440:
437:
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431:
418:
417:
404:(Ω;
396:
393:
392:
391:
381:weakly-∗
377:
376:
375:
374:
363:
360:
355:
351:
347:
342:
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336:
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318:
317:
313:
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273:
269:
262: in
258:
255:
250:
246:
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237:
234:
230:
216:
215:
210:(Ω;
201:
195:
174:
169:(Ω;
164:Lebesgue space
139:(Ω;
118:bounded domain
113:
110:
77:Sobolev spaces
63:
62:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
1092:
1081:
1078:
1076:
1075:Banach spaces
1073:
1072:
1070:
1055:
1047:
1046:
1043:
1037:
1034:
1032:
1029:
1027:
1026:Weak topology
1024:
1022:
1019:
1017:
1014:
1012:
1009:
1008:
1006:
1002:
995:
991:
988:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
956:
953:
951:
950:Index theorem
948:
946:
943:
941:
938:
936:
933:
932:
930:
926:
920:
917:
915:
912:
911:
909:
907:Open problems
905:
899:
896:
894:
891:
889:
886:
884:
881:
879:
876:
874:
871:
870:
868:
864:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
820:
818:
815:
813:
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809:
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803:
797:
794:
792:
789:
787:
784:
782:
779:
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769:
767:
764:
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753:
751:
749:
745:
735:
732:
730:
727:
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722:
719:
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708:
706:
703:
701:
698:
697:
695:
691:
685:
682:
680:
677:
675:
672:
670:
667:
665:
662:
660:
657:
655:
652:
650:
647:
645:
642:
640:
637:
636:
633:
630:
626:
621:
617:
613:
606:
601:
599:
594:
592:
587:
586:
583:
579:
574:
571:
566:
562:
557:
552:
549:: 10–46, 94.
548:
544:
540:
538:
531:
530:
526:
521:
517:
513:
512:
495:
490:
482:
476:
469:
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456:
450:
441:
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435:
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421:
420:
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411:
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403:
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379:
378:
361:
358:
353:
349:
334:
322:
321:
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292:
282:
271:
267:
256:
253:
248:
244:
232:
220:
219:
218:
217:
213:
209:
204:
200:
196:
193:
189:
188:Borel measure
186:
182:
178:
175:
172:
168:
165:
161:
158:
157:
156:
154:
150:
146:
145:ordered pairs
142:
138:
135:
131:
127:
124:-dimensional
123:
119:
111:
109:
107:
104:
100:
96:
92:
88:
85:
84:mathematician
82:
78:
74:
73:Souček spaces
70:
59:
56:November 2022
50:is available.
49:
45:
39:
38:
34:
29:This article
27:
18:
17:
1016:Balanced set
990:Distribution
928:Applications
781:Krein–Milman
766:Closed graph
577:
546:
542:
536:
515:
410:Banach space
405:
401:
385:
211:
207:
202:
198:
180:
176:
170:
166:
162:lies in the
159:
152:
148:
140:
136:
134:Souček space
133:
128:with smooth
121:
115:
98:
90:
72:
66:
53:
48:Editing help
30:
945:Heat kernel
935:Hardy space
842:Trace class
756:Hahn–Banach
718:Topological
214:) such that
106:subsequence
87:Jiří Souček
69:mathematics
1069:Categories
878:C*-algebra
693:Properties
527:References
395:Properties
194:of Ω;
112:Definition
852:Unbounded
847:Transpose
805:Operators
734:Separable
729:Reflexive
714:Algebraic
700:Barrelled
565:0528-2195
487:‖
480:‖
461:‖
454:‖
448:‖
430:‖
346:∇
341:∞
338:→
280:Ω
239:∞
236:→
155:), where
93:is not a
1054:Category
866:Algebras
748:Theorems
705:Complete
674:Schwartz
620:glossary
416:given by
130:boundary
97:; since
857:Unitary
837:Nuclear
822:Compact
817:Bounded
812:Adjoint
786:Min–max
679:Sobolev
664:Nuclear
654:Hilbert
649:Fréchet
614: (
573:0313798
408:) is a
388:-valued
192:closure
190:on the
185:regular
183:) is a
151:,
132:. The
832:Normal
669:Orlicz
659:Hölder
639:Banach
628:Spaces
616:topics
563:
31:is in
644:Besov
81:Czech
37:prose
992:(or
710:Dual
561:ISSN
518:and
414:norm
33:list
551:doi
331:lim
316:and
229:lim
120:in
67:In
1071::
618:–
570:MR
559:.
547:97
545:.
541:.
451::=
173:);
71:,
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720:)
716:/
712:(
622:)
604:e
597:t
590:v
567:.
553::
537:k
516:L
496:,
491:M
483:v
477:+
470:1
466:L
457:u
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442:v
439:,
436:u
433:(
406:R
402:W
386:R
362:v
359:=
354:k
350:u
335:k
298:)
293:m
288:R
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277:(
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268:L
257:u
254:=
249:k
245:u
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203:k
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181:u
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147:(
141:R
137:W
122:n
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