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Behnke–Stein theorem

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282: 85: 131: 323: 31: 347: 38: 352: 156:. Though historically this theorem was in fact used to solve the Levi problem, and the theorem itself was proved using the 17: 342: 259: 48: 316: 269: 90: 264: 309: 181: 142: 297: 160:. This theorem again holds for Stein manifolds, but it is not known if it holds for Stein space. 289: 186: 157: 134: 8: 221:
Coltoiu, Mihnea (2009). "The Levi problem on Stein spaces with singularities. A survey".
149: 250: 222: 203: 184:(1939). "Konvergente Folgen von Regularitätsbereichen und die Meromorphiekonvexität". 207: 195: 177: 138: 152:
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
93: 51: 137:is again a domain of holomorphy. It was proved by 125: 79: 334: 251:Creative Commons Attribution/Share-Alike License 45:states that a union of an increasing sequence 317: 80:{\displaystyle G_{k}\subset \mathbb {C} ^{n}} 176: 324: 310: 226: 67: 241:This article incorporates material from 220: 32:Behnke–Stein theorem on Stein manifolds 14: 335: 257: 276: 126:{\displaystyle G_{k}\subset G_{k+1}} 24: 25: 364: 280: 249:, which is licensed under the 214: 170: 13: 1: 163: 348:Theorems in complex analysis 296:. You can help Knowledge by 7: 353:Mathematical analysis stubs 265:Encyclopedia of Mathematics 37:In mathematics, especially 10: 369: 275: 29: 343:Several complex variables 39:several complex variables 30:Not to be confused with 292:–related article is a 258:Chirka, E.M. (2001) , 127: 81: 290:mathematical analysis 187:Mathematische Annalen 135:domains of holomorphy 128: 82: 243:Behnke-Stein theorem 150:pseudoconvex domains 91: 49: 43:Behnke–Stein theorem 18:Behnke-Stein theorem 200:10.1007/BF01597355 123: 77: 305: 304: 16:(Redirected from 360: 326: 319: 312: 284: 277: 272: 260:"Stein manifold" 233: 232: 230: 218: 212: 211: 174: 158:Oka–Weil theorem 132: 130: 129: 124: 122: 121: 103: 102: 86: 84: 83: 78: 76: 75: 70: 61: 60: 21: 368: 367: 363: 362: 361: 359: 358: 357: 333: 332: 331: 330: 237: 236: 219: 215: 175: 171: 166: 139:Heinrich Behnke 111: 107: 98: 94: 92: 89: 88: 71: 66: 65: 56: 52: 50: 47: 46: 35: 28: 23: 22: 15: 12: 11: 5: 366: 356: 355: 350: 345: 329: 328: 321: 314: 306: 303: 302: 285: 274: 273: 255: 235: 234: 213: 168: 167: 165: 162: 120: 117: 114: 110: 106: 101: 97: 74: 69: 64: 59: 55: 26: 9: 6: 4: 3: 2: 365: 354: 351: 349: 346: 344: 341: 340: 338: 327: 322: 320: 315: 313: 308: 307: 301: 299: 295: 291: 286: 283: 279: 278: 271: 267: 266: 261: 256: 254: 252: 248: 244: 239: 238: 229: 224: 217: 209: 205: 201: 197: 193: 189: 188: 183: 179: 173: 169: 161: 159: 155: 151: 146: 144: 140: 136: 118: 115: 112: 108: 104: 99: 95: 72: 62: 57: 53: 44: 40: 33: 19: 298:expanding it 287: 263: 240: 216: 191: 185: 172: 154:Levi problem 147: 42: 36: 194:: 204–216. 337:Categories 247:PlanetMath 178:Behnke, H. 164:References 143:Karl Stein 270:EMS Press 228:0905.2343 208:123982856 182:Stein, K. 145:in 1938. 105:⊂ 63:⊂ 87:(i.e., 206:  41:, the 288:This 223:arXiv 204:S2CID 133:) of 294:stub 141:and 245:on 196:doi 192:116 339:: 268:, 262:, 202:. 190:. 180:; 325:e 318:t 311:v 300:. 253:. 231:. 225:: 210:. 198:: 119:1 116:+ 113:k 109:G 100:k 96:G 73:n 68:C 58:k 54:G 34:. 20:)

Index

Behnke-Stein theorem
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

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