Скачать с ютуб Lino F. Resendis Ocampo: Recovering bicomplex holomorphic functions without Cauchy Riemann equations в хорошем качестве

Lino F. Resendis Ocampo: Recovering bicomplex holomorphic functions without Cauchy Riemann equations

HyperComplex Seminar, 17 Sep 2024 Abstract. In [Sha], Shaw writes a proof of a classical statement of Ahlfors ([Ah],p. 27-28) concerning with the reconstruction of a holomorphic function from its real or imaginary parts (without Cauchy-Riemann equations). In the same paper, Shaw recall the notion of complex harmonic function, that is, a smooth function U : Ω ⊂ C2 → C, in the domain Ω that satises the complex type Laplace equation: (formula) ∂2U/∂z21+ ∂2U/∂z22= 0. In this talk we give another proof of the statement of Ahlfors and we show that the bicomplex holomorphic theory is well suited for complex harmonic functions. Moreover, we recover V , a complex conjugate harmonic function of U , such that U + jV is a bicomplex holomorphic function, see [LuShStVa], (V is recovered without complex Cauchy-Riemann equations). Keywords and phrases: complex harmonic function, bicomplex holomorphic function References [Ah] L. V. Ahlfors,Complex analysis, Mc-Graw-Hill, New York, 3rd. 1979 [LuShStVa] M. E. Luna-Elizarraraz; M. Shapiro; Daniele C. Struppa; Adrián Vajiac Bicomplex Holomorphic Functions: The Algebra, Geometry and Analysis, Frontiers in Mathematics, Birkhäuser, 2015. [Sha] W. T. Shaw Recovering Holomorphic Functions from Their Real or Imaginary Parts without the Cauchy-Riemann Equations, SIAM REVIEW, Vol. 46. no. 4. pp. 717-728.