1550251515-Classical_Complex_Analysis__Gonzalez_

Differentiation 385 open. In what follows we shall use the term open function in the sense of strongly open. A function f: A --+ ...

386 Chapter6 Theorem 6.33 Let A be any open set, and let a E A. If f is continuous on A and open on A - {a}, then f is open on A ...

Differentiation and since I( - zl = l(zo -z) + (( -zo)I > r -^1 / 2 r = %r it follows that l f(zo)-f(z) _ f(()-f(z)I <e Zo ...

388 Chapter^6 Theorem 6.38 If f is analytic in a region R and K is a compact subset of R, then the increment ratio .6.f / .6.z t ...

Differentiation 389 is bounded in D. In 1925, H. Looman [80] showed that the boundedness condition (6.23-1) can be replaced by t ...

390 Chapter^6 in D. By improving on the last two results Menchoff was able to obtain minimal conditions for analyticity. For thi ...

Differentiation 391 problems in mathematical physics that depend on the solution of equations of the same type. Other authors ha ...

392 Chapter 6 The function u + iv may be considered as a complex function of the point (p, q) on the surface S, and the system ( ...

Differentiation 393 Equations ( 6.24-6) are identical (mu ta tis mutandi) to the Beltrami equations (6.24-2). For we may let, as ...

394 Chapter6 conjugate when the equation . df dF dn da holds at every point of a certain region, where n is any direction whatev ...

Differentiation 395 The following assumptions are made concerning the coefficients O'k, 7k: (1) They are defined for all values ...

396 Chapter6 Bers says that w( z) has at Zo the (F, G)-derivative w( Zo) if the finite limit .( ) 1 . w(z)-,\oF(z)-μoG(z) w zo = ...

Differentiation 397 an equation of the form w.z+Aw+Bw=F (6.24-15) where A, B, and Fare of class LP with p > 2, i.e., of measu ...

398 Chapter^6 and Ux =A [Vy Wyl' Vx = A [ Wy Uy] , Wx =A [Uy Vy l Vz Wz Wz Uz Uz Vz Uy=,;\ [ Vz Wz], Vy = ,;\ [ Wz Uz] , Wy = ,\ ...

Differentiation . The element of arc of 'Y at p is given by ds^2 = dx · dx = L(dxi)^2 i 399 the dxi being direction numbers of t ...

400 Chapter^6 Solving for aii, we get .. p2 a'^1 = -yAi; (6.24-19) where Aij is the cofactor of aii in J. Since 0 .~] = p2n p2 w ...

Differentiation 401 which is a generalization of the Laplace equation. (1) J. D. Abercrombie in [1] uses M. Itoh bicomplex numbe ...

402 Chapter^6 L. Bers, Partial differential equations and generalized analytic functions, Proc. Nat. Acad. Sci., 36 {1950), 130 ...

Differentiation 403 P. Dentoni, Sulla funzioni monogene nella algebra noncommutative, Rend. Mat. Appl., 26 (1967), 403-421. P. ...

404 Chapter^6 M. 0. Gonzalez, Some topics on differentiation and integration of functions of a complex variable, Rev. Univ. Nae ...