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Behnke–Stein theorem

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271: 74: 120: 20: 312: 336: 27: 341: 331: 305: 145:. Though historically this theorem was in fact used to solve the Levi problem, and the theorem itself was proved using the 258: 253: 248: 298: 170: 131: 37: 79: 278: 175: 239: 146: 123: 138: 211: 192: 149:. This theorem again holds for Stein manifolds, but it is not known if it holds for Stein space. 282: 184: 166: 127: 210:
Coltoiu, Mihnea (2009). "The Levi problem on Stein spaces with singularities. A survey".
173:(1939). "Konvergente Folgen von Regularitätsbereichen und die Meromorphiekonvexität". 325: 196: 142: 141:
is pseudoconvex and so it can be proven using that fact and the solution of the
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Theorem in mathematics about unions of domains of holomorphy
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This is related to the fact that an increasing union of
286: 82: 40: 126:is again a domain of holomorphy. It was proved by 114: 68: 240:Creative Commons Attribution/Share-Alike License 34:states that a union of an increasing sequence 306: 69:{\displaystyle G_{k}\subset \mathbb {C} ^{n}} 8: 313: 299: 215: 100: 87: 81: 60: 56: 55: 45: 39: 230:This article incorporates material from 158: 21:Behnke–Stein theorem on Stein manifolds 7: 267: 265: 115:{\displaystyle G_{k}\subset G_{k+1}} 285:. You can help Knowledge (XXG) by 14: 269: 238:, which is licensed under the 1: 337:Theorems in complex analysis 342:Mathematical analysis stubs 254:Encyclopedia of Mathematics 26:In mathematics, especially 358: 264: 18: 332:Several complex variables 28:several complex variables 19:Not to be confused with 281:–related article is a 247:Chirka, E.M. (2001) , 116: 70: 279:mathematical analysis 176:Mathematische Annalen 124:domains of holomorphy 117: 71: 232:Behnke-Stein theorem 139:pseudoconvex domains 80: 38: 32:Behnke–Stein theorem 189:10.1007/BF01597355 112: 66: 294: 293: 349: 315: 308: 301: 273: 266: 261: 249:"Stein manifold" 222: 221: 219: 207: 201: 200: 163: 147:Oka–Weil theorem 121: 119: 118: 113: 111: 110: 92: 91: 75: 73: 72: 67: 65: 64: 59: 50: 49: 357: 356: 352: 351: 350: 348: 347: 346: 322: 321: 320: 319: 246: 226: 225: 209: 208: 204: 165: 164: 160: 155: 128:Heinrich Behnke 96: 83: 78: 77: 54: 41: 36: 35: 24: 17: 12: 11: 5: 355: 353: 345: 344: 339: 334: 324: 323: 318: 317: 310: 303: 295: 292: 291: 274: 263: 262: 244: 224: 223: 202: 157: 156: 154: 151: 109: 106: 103: 99: 95: 90: 86: 63: 58: 53: 48: 44: 15: 13: 10: 9: 6: 4: 3: 2: 354: 343: 340: 338: 335: 333: 330: 329: 327: 316: 311: 309: 304: 302: 297: 296: 290: 288: 284: 280: 275: 272: 268: 260: 256: 255: 250: 245: 243: 241: 237: 233: 228: 227: 218: 213: 206: 203: 198: 194: 190: 186: 182: 178: 177: 172: 168: 162: 159: 152: 150: 148: 144: 140: 135: 133: 129: 125: 107: 104: 101: 97: 93: 88: 84: 61: 51: 46: 42: 33: 29: 22: 287:expanding it 276: 252: 229: 205: 180: 174: 161: 143:Levi problem 136: 31: 25: 183:: 204–216. 326:Categories 236:PlanetMath 167:Behnke, H. 153:References 132:Karl Stein 259:EMS Press 217:0905.2343 197:123982856 171:Stein, K. 134:in 1938. 94:⊂ 52:⊂ 76:(i.e., 195:  30:, the 277:This 212:arXiv 193:S2CID 122:) of 283:stub 130:and 234:on 185:doi 181:116 328:: 257:, 251:, 191:. 179:. 169:; 314:e 307:t 300:v 289:. 242:. 220:. 214:: 199:. 187:: 108:1 105:+ 102:k 98:G 89:k 85:G 62:n 57:C 47:k 43:G 23:.

Index

Behnke–Stein theorem on Stein manifolds
several complex variables
domains of holomorphy
Heinrich Behnke
Karl Stein
pseudoconvex domains
Levi problem
Oka–Weil theorem
Behnke, H.
Stein, K.
Mathematische Annalen
doi
10.1007/BF01597355
S2CID
123982856
arXiv
0905.2343
Behnke-Stein theorem
PlanetMath
Creative Commons Attribution/Share-Alike License
"Stein manifold"
Encyclopedia of Mathematics
EMS Press
Stub icon
mathematical analysis
stub
expanding it
v
t
e

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