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Hardy's theorem

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This article incorporates material from Hardy's theorem on
266: 227: 116: 89: 65: 41: 278: 248: 210: 95: 71: 47: 165: 327:Creative Commons Attribution/Share-Alike License 8: 265: 226: 201: 184: 156: 151: 132: 115: 88: 64: 40: 316:. Springer-Verlag, New York, New York. 7: 314:Functions of One Complex Variable I 14: 55:be a holomorphic function on the 256:then this function is strictly 325:, which is licensed under the 193: 174: 126: 120: 1: 301:Hadamard three-circle theorem 343:Theorems in complex analysis 260:and is a convex function of 249:{\displaystyle 0<r<R,} 59:centered at zero and radius 28:describing the behavior of 359: 312:John B. Conway. (1978) 280: 279:{\displaystyle \log r} 250: 212: 97: 73: 49: 281: 251: 213: 98: 74: 50: 30:holomorphic functions 264: 225: 114: 87: 63: 39: 164: 276: 246: 208: 147: 107:. If one defines 93: 83:, and assume that 69: 45: 296:Maximum principle 145: 105:constant function 96:{\displaystyle f} 72:{\displaystyle R} 48:{\displaystyle f} 350: 285: 283: 282: 277: 255: 253: 252: 247: 217: 215: 214: 209: 200: 196: 192: 191: 163: 155: 146: 144: 133: 102: 100: 99: 94: 78: 76: 75: 70: 54: 52: 51: 46: 26:complex analysis 358: 357: 353: 352: 351: 349: 348: 347: 333: 332: 309: 292: 262: 261: 223: 222: 180: 170: 166: 137: 112: 111: 85: 84: 61: 60: 37: 36: 24:is a result in 22:Hardy's theorem 12: 11: 5: 356: 354: 346: 345: 335: 334: 318: 317: 308: 305: 304: 303: 298: 291: 288: 275: 272: 269: 245: 242: 239: 236: 233: 230: 219: 218: 207: 204: 199: 195: 190: 187: 183: 179: 176: 173: 169: 162: 159: 154: 150: 143: 140: 136: 131: 128: 125: 122: 119: 92: 68: 44: 13: 10: 9: 6: 4: 3: 2: 355: 344: 341: 340: 338: 331: 330: 328: 324: 315: 311: 310: 306: 302: 299: 297: 294: 293: 289: 287: 273: 270: 267: 259: 243: 240: 237: 234: 231: 228: 205: 202: 197: 188: 185: 181: 177: 171: 167: 160: 157: 152: 148: 141: 138: 134: 129: 123: 117: 110: 109: 108: 106: 90: 82: 81:complex plane 66: 58: 42: 33: 31: 27: 23: 19: 320: 319: 313: 220: 34: 21: 15: 18:mathematics 323:PlanetMath 307:References 258:increasing 271:⁡ 206:θ 189:θ 161:π 149:∫ 142:π 103:is not a 57:open ball 337:Category 290:See also 79:in the 238:< 232:< 221:for 35:Let 268:log 32:. 16:In 339:: 286:. 20:, 329:. 274:r 244:, 241:R 235:r 229:0 203:d 198:| 194:) 186:i 182:e 178:r 175:( 172:f 168:| 158:2 153:0 139:2 135:1 130:= 127:) 124:r 121:( 118:I 91:f 67:R 43:f

Index

mathematics
complex analysis
holomorphic functions
open ball
complex plane
constant function
increasing
Maximum principle
Hadamard three-circle theorem
PlanetMath
Creative Commons Attribution/Share-Alike License
Category
Theorems in complex analysis

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