Holomorphic Functions in the Plane and n-dimensional Space

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Springer Science & Business Media, Nov 16, 2007 - Mathematics - 394 pages
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Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.

 

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Contents

IV
2
V
3
VI
10
VII
13
VIII
15
IX
16
X
24
XII
26
LXXI
181
LXXII
184
LXXIII
186
LXXV
188
LXXVI
191
LXXVII
194
LXXVIII
196
LXXIX
202

XIII
30
XIV
31
XV
33
XVI
37
XVII
42
XVIII
46
XIX
47
XX
49
XXI
50
XXII
52
XXIII
55
XXIV
58
XXV
61
XXVI
63
XXVII
66
XXVIII
67
XXIX
71
XXX
73
XXXI
74
XXXII
79
XXXIII
83
XXXIV
87
XXXV
88
XXXVI
90
XXXVII
95
XXXVIII
96
XXXIX
97
XL
101
XLI
104
XLII
107
XLIII
108
XLIV
109
XLV
114
XLVI
118
XLVII
124
XLVIII
125
XLIX
126
L
129
LI
131
LII
133
LIII
138
LIV
141
LV
144
LVI
146
LVII
147
LVIII
149
LIX
151
LXI
156
LXII
159
LXIII
160
LXIV
161
LXV
162
LXVI
164
LXVII
167
LXVIII
169
LXIX
173
LXX
175
LXXX
203
LXXXII
207
LXXXIII
213
LXXXIV
215
LXXXV
218
LXXXVI
219
LXXXVII
221
LXXXVIII
223
LXXXIX
225
XC
229
XCI
234
XCII
239
XCIII
244
XCIV
249
XCV
252
XCVI
255
XCVII
259
XCVIII
265
XCIX
267
C
270
CI
274
CII
276
CIII
279
CIV
285
CV
287
CVI
291
CVII
296
CVIII
298
CIX
302
CX
307
CXI
321
CXII
323
CXIII
324
CXIV
329
CXV
336
CXVI
338
CXVII
339
CXVIII
341
CXIX
351
CXX
352
CXXI
354
CXXII
355
CXXIII
357
CXXV
358
CXXVI
359
CXXVII
360
CXXVIII
361
CXXX
363
CXXXII
364
CXXXIII
368
CXXXIV
370
CXXXV
374
CXXXVI
375
CXXXVII
377
CXXXVIII
385
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