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Talk:Time-scale calculus

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84: 255: 74: 53: 179: 158: 189: 373:. People have considered coefficients which are measures. That is, you look at the ode in a weak sense after performing the Lebesgue-Stieltjes integral on both sides and, voila, you can treat differential and difference equations at the same time if you take either a purely absolutely continuous or a pure point measure for the weight, respectively. See for example the books by Atkinson from 1964 or by Mingarelli on 22: 315:
I have added Hilger's PhD thesis as a reference, but I was unable to locate an electronic copy of it to link. If anyone can provide a link to a copy of it (or even just a doi number), it would be much
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at all isolated points with weight given by the graininess. Then it seems to me that the Hilger derivative is just the
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with respect to this measure (i.e. the inverse operation to the corresponding Lebesgue-Stieltjes integral)? --
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and the time scale delta-integral have been combined to get a Riemann-Stieltjes integral on time scales.
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s can be treated on an equal footing. Can you say the Riemann-Stieltjes integral is useful for this ?
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The broken link has been fixed. The university's address had changed from web.umr.edu to web.mst.edu
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions
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The special issue, the first link under further reading, is a dead link.
377:(Springer LNM 989) from 1983. Moreover, consider the measure which is 207: 340: 15: 253: 101:, a collaborative effort to improve the coverage of 369:I am not an expert on this, but take for example 346:The main point of Time-scale calculus is that 381:restricted to the dense points plus a sum of 341:The Riemann-Stieltjes integral on time scales 8: 206:, which collaborates on articles related to 19: 152: 47: 154: 49: 434:Systems articles in dynamical systems 7: 262:This article is within the field of 200:This article is within the scope of 95:This article is within the scope of 38:It is of interest to the following 14: 419:Low-priority mathematics articles 115:Knowledge:WikiProject Mathematics 414:Start-Class mathematics articles 187: 177: 156: 118:Template:WikiProject Mathematics 82: 72: 51: 20: 429:Mid-importance Systems articles 240:This article has been rated as 135:This article has been rated as 1: 220:Knowledge:WikiProject Systems 109:and see a list of open tasks. 439:WikiProject Systems articles 424:Start-Class Systems articles 399:13:20, 27 October 2010 (UTC) 364:07:52, 27 October 2010 (UTC) 223:Template:WikiProject Systems 326:17:20, 9 October 2009 (UTC) 455: 337:Riemann-Stieltjes integral 331:Riemann-Stieltjes integral 246:project's importance scale 310:10:05, 3 April 2009 (UTC) 295:00:20, 3 April 2009 (UTC) 261: 239: 172: 134: 67: 46: 387:Radon-Nikodym derivative 371:Sturm-Liouville problems 141:project's priority scale 98:WikiProject Mathematics 258: 195:Systems science portal 28:This article is rated 352:differential equation 257: 348:difference equations 121:mathematics articles 203:WikiProject Systems 259: 90:Mathematics portal 34:content assessment 278: 277: 274: 273: 270: 269: 264:Dynamical systems 151: 150: 147: 146: 446: 379:Lebesgue measure 228: 227: 226:Systems articles 224: 221: 218: 197: 192: 191: 190: 181: 174: 173: 168: 160: 153: 123: 122: 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 454: 453: 449: 448: 447: 445: 444: 443: 404: 403: 333: 283: 225: 222: 219: 216: 215: 212:systems science 193: 188: 186: 166: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 452: 450: 442: 441: 436: 431: 426: 421: 416: 406: 405: 402: 401: 383:Dirac measures 356:89.241.225.148 332: 329: 313: 312: 282: 279: 276: 275: 272: 271: 268: 267: 260: 250: 249: 242:Mid-importance 238: 232: 231: 229: 199: 198: 182: 170: 169: 167:Mid‑importance 161: 149: 148: 145: 144: 133: 127: 126: 124: 107:the discussion 94: 93: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 451: 440: 437: 435: 432: 430: 427: 425: 422: 420: 417: 415: 412: 411: 409: 400: 396: 392: 388: 384: 380: 376: 372: 368: 367: 366: 365: 361: 357: 353: 349: 344: 342: 338: 330: 328: 327: 323: 319: 311: 307: 303: 299: 298: 297: 296: 292: 288: 280: 265: 256: 252: 251: 247: 243: 237: 234: 233: 230: 213: 209: 205: 204: 196: 185: 183: 180: 176: 175: 171: 165: 162: 159: 155: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 374: 345: 334: 316:appreciated. 314: 284: 241: 201: 137:Low-priority 136: 96: 62:Low‑priority 40:WikiProjects 112:Mathematics 103:mathematics 59:Mathematics 30:Start-class 408:Categories 302:Charvest 281:untitled 391:Mathuvw 318:Apophos 244:on the 217:Systems 208:systems 164:Systems 139:on the 36:scale. 287:RhysU 395:talk 360:talk 350:and 335:The 322:talk 306:talk 291:talk 210:and 236:Mid 131:Low 410:: 397:) 362:) 343:. 324:) 308:) 293:) 393:( 358:( 320:( 304:( 289:( 266:. 248:. 214:. 143:. 42::

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RhysU
talk
00:20, 3 April 2009 (UTC)
Charvest
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10:05, 3 April 2009 (UTC)

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