# TAILIEUCHUNG - The Riemann Hilbert problem for generalized Q-holomorphic functions

## We clearly do not investigate the conditions under which there are continuous solution in G even when the boundary vector family has positive index. In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions. | Turk J Math 34 (2010) , 167 – 180. ¨ ITAK ˙ c TUB doi: The Riemann Hilbert problem for generalized Q-holomorphic functions Sezayi Hızlıyel and Mehmet C ¸ a˘glıyan Abstract In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Qholomorphic functions. Key Words: Generalized Beltrami systems, Q-Holomorphic functions, Riemann Hilbert problem. 1. Introduction In [6] A. Douglis developed an analogue of analytic functions theory for more general elliptic systems in the plane of the form wx + iwy + aEwx + bEwy = 0, (1) where E is an m × m constant matrix, w is an m × 1 vector, and a and b are complex valued functions of x and y . Subsequently in [5] B. Bojarski˘ı extended the function theory of Douglis to a system which he wrote in the form (2) wz = qwz . He assumed that the variable m × m matrix q is “lower diagonal with all eigenvalues of q having magnitude less than 1 . The systems (1) and (2) are natural ones to consider because they arise from the reduction of general elliptic systems of ﬁrst order in the plane to a standard canonical form. Douglis and Bojarski˘ı theory has been used to study the elliptic systems of more general form: wz − qwz = aw + bw. Solutions of this equation were called generalized (or pseudo) hyperanalytic functions. Works in this direction appear in [7, 8, 10, 11]. These results extend the generalized (or “pseudo”) analytic function theory of Bers [4] and Vekua [17]. Also, the classical boundary value problems for analytic functions were extended to the generalized hyperanalytic functions. A good survey of the methods encountered in the hyperanalytic case may be found in [3, 9], see also [1, 2]. AMS Mathematics Subject Classiﬁcation: 30G20, 30G35, 35J55. 167 ˘ HIZLIYEL, C ¸ AGLIYAN In [13], Hile noticed that what appears to be the essential property of the elliptic systems in the plane for which one can obtain a useful extension of analytic function theory is the self .

TÀI LIỆU LIÊN QUAN
14    27    0
TÀI LIỆU XEM NHIỀU
3    6372    87
14    4501    234
8    3919    1442
8    3612    1
2    2981    24
24    2964    55
9    2731    3
35    2710    135
29    2596    73
8    2483    20
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
20    37    0    18-05-2021
7    73    0    18-05-2021
3    35    0    18-05-2021
35    29    0    18-05-2021
10    48    0    18-05-2021
10    28    0    18-05-2021
1049    17    0    18-05-2021
6    32    0    18-05-2021
2    17    0    18-05-2021
4    23    0    18-05-2021
TÀI LIỆU HOT
8    3919    1442
112    840    394
122    814    296
14    4501    234
20    1624    209
36    1307    199
35    1111    196
21    2052    177
16    2081    176
171    1095    168