Colombeau products of distributions
In this paper, some products of distributions are derived. The results are obtained in Colombeau algebra of generalized functions, which is the most relevant algebraic construction for dealing with Schwartz distributions. Colombeau algebra $${\mathcal{G}}({\mathbf{R}})$$G(R) contains the space $${\mathcal{D}'}({\mathbf{R}})$$D′(R) of Schwartz distributions as a subspace, and has a notion of 'association’ that allows us to evaluate the results in terms of distributions.
Results on the Colombeau Products of the Distribution x+−r−1/2 with the Distributions x−−k−1/2 and x−k−1/2
Results on the products of the distribution x+−r−1/2 with the distributions x−−k−1/2 and x−k−1/2 are obtained in the differential algebra G(ℝ) of Colombeau generalized functions, which contains the space D′(ℝ) of Schwartz distributions as a subspace; in this algebra the notion of association is defined, which is a faithful generalization of weak equality in G(ℝ). This enables treating the results in terms of distributions again.
Subject index
Adoptive immunotherapy A1, A63, A63, A64, A64, A65, A66, A68, A69, A69, A70, A70, A71, A71, A72, A72, A73, A73, A74, A75, A76, A78, A79, A79, A7, A80, A80, A81, A81, A82, A84, A85, A86, A86, A88, A88, A89, A90, A90, A91, A92, A93, A93, A94, A95, A95, A96, A96, A97, A97, A98, A98, A99, A99, A102, A103, A104, A104, A166, A167, A169, A170, A174, A177, A179, A181, A182, A199, A204, A205, A21, A215, A220, A231, A231, A243, A251, A254, A25, A276, A287, A304, A307, A310, A315, A316, A316, A329, A331, A333, A357, A358, A369, A405, A441, A442, A458, A458, A459, A459, A461, A461, A463, A468, A468, A479, A492, A497, A497, A56, A58, A58, A59, A60, A60, A61, 1, 100, 101, 102, 103, 104, 106, 109, 111, 112, 113, 114, 115, 116, 117, 119, 120, 122, 123, 124, 125, 127, 128, 129, 13, 130, 131, 133, 134, 136, 139, 140, 141, 142, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 163, 164, 165, 166, 167, 169, 173, 174, 175, 272, 273, 278, 280, 285, 290, 293, 297, 298, 324, 333, 335, 35, 353, 360, 379, 380, 400, 414, 418, 42, 454, 470, 493, 500, 504, 513, 515, 516, 542, 545, 549, 598, 599, 614, 675, 737, 739, 764, 765, 766, 767, 770, 771, 772, 780, 781, 801, 822, 830, 831, 89, 91, 92, 94, 95, 96, 98 Angiogenesis A108, A155, A171, A200, A201, A214, A228, A265, A305, A349, A350, A359, A410, A47, A48, A480, A483, A519, A5, 181, 257, 281, 327, 328, 351, 374, 435, 495, 583, 584, 602, 683, 76, 78, 802, 808, 873, 9 Antibody A7, A73, A81, A86, A91, A8, A99, A9, A104, A108, A108, A109, A109, A111, A115, A119, A126, A128, A130, A135, A138, A141, A144, A151, A153, A159, A160, A163, A164, A164, A171, A172, A175, A176, A2, A187, A193, A193, A195, A195, A198, A199, A20, A209, A212, A225, A229, A230, A23, A233, A233, A235, A239, A239, A240, A242, A244, A244, A245, A245, A246, A247, A247, A24, A250, A256, A260, A261, A266, A267, A268, A269, A273, A275, A286, A288, A292, A293, A296, A299, A300, A307, A3, A308, A31, A318, A324, A35, A334, A334, A336, A338, A339, A342, A343, A344, A344, A346, A346, A351, A351, A353, A356, A360, A361, A363, A368, A369, A370, A371, A372, A372, A373, A374, A376, A377, A378, A378, A379, A379, A380, A380, A388, A391, A399, A399, A41, A402, A410, A410, A411, A412, A414, A417, A418, A419, A419, A420, A422, A422, A423, A426, A427, A428, A428, A430, A431, A432, A434, A434, A435, A446, A454, A455, A459, A463, A465, A468, A468, A469, A474, A481, A483, A50, A486, A487, A491, A502, A502, A504, A507, A507, A508, A510, A511, A512, A512, A516, 12, 122, 133, 141, 151, 16, 167, 17, 174, 181, 182, 184, 185, 188, 195, 203, 210, 215, 218, 227, 231, 237, 243, 250, 253, 261, 262, 265, 267, 268, 281, 282, 287, 288, 3, 305, 313, 315, 317, 318, 323, 325, 34, 342, 348, 369, 377, 378, 38, 384, 385, 387, 393, 394, 395, 399, 401, 402, 403, 404, 405, 406, 407, 41, 412, 421, 428, 429, 438, 439, 442, 443, 450, 453, 469, 472, 476, 478, 480, 483, 486, 499, 5, 501, 51, 519, 531, 55, 550, 552, 557, 561, 562, 569, 571, 572, 573, 576, 578, 586, 587, 590, 594, 603, 605, 607, 612, 615, 616, 617, 618, 619, 621, 622, 626, 629, 630, 631, 632, 633, 634, 635, 647, 653, 665, 666, 67, 670, 683, 684, 686, 687, 690, 693, 696, 697, 698, 699, 702, 703, 704, 711, 713, 714, 715, 718, 721, 722, 725, 726, 727, 745, 757, 760, 766, 772, 776, 780, 781, 785, 793, 804, 808, 81, 812, 814, 820, 842, 843, 846, 851, 852, 853, 856, 858, 860, 861, 869 Antigen presenting cells A67, A79, A80, A92, A95, A96, A99, A99, A101, A102, A102, A108, A108, A111, A129, A139, A160, A166, A177, A178, A183, A191, A191, A213, A220, A221, A245, A254, A256, A262, A266, A275, A314, A322, A327, A328, A35, A335, A345, A359, A359, A360, A361, A364, A366, A368, A369, A371, A372, A403, A409, A411, A411, A418, A422, A433, A449, A48, A468, A471, A472, A4, A50, A495, A502, A506, A513, A514, A515, 108, 128, 130, 153, 157, 160, 166, 167, 168, 169, 170, 181, 182, 188, 217, 235, 263, 271, 290, 291, 299, 310, 311, 349, 360, 362, 404, 418, 421, 431, 438, 453, 510, 526, 538, 540, 55, 553, 575, 601, 602, 603, 605, 610, 611, 612, 615, 617, 618, 672, 682, 685, 686, 695, 703, 724, 748, 78, 780, 787, 790, 8, 81, 828, 842, 849, 862, 864, 868 Autoimmunity A8, A116, A15, A180, A181, A22, A380, A387, A394, A395, A402, A408, A502, A510, 16, 197, 27, 295, 296, 37, 637, 645, 657, 658, 671, 680, 843, 856