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A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory; summation methods; and the spectral synthesis theorem of L. Schwartz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic analysis. By providing an overview of current research and open problems, as well as topics that have wide applications in engineering, this book should be of interest to mathematicians and applied mathematicians, as well as to graduate students beginning their research. [Back cover]

Functions of complex variables --- Harmonic analysis --- Functions, Entire --- Fonctions d'une variable complexe. --- Analyse harmonique (mathématiques) --- Fonctions entières.

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Fonctions d'une variable complexe. --- Functions of complex variables. --- Fonctions entières. --- Functions, Entire. --- Distribution des valeurs, Théorie de la --- Value distribution theory --- Fonctions entières. --- Distribution des valeurs, Théorie de la

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The present monograph grew out of the fifth set of Hermann Weyl Lectures, given by Professor Griffiths at the Institute for Advanced Study, Princeton, in fall 1974.In Chapter 1 the author discusses Emile Borel's proof and the classical Jensen theorem, order of growth of entire analytic sets, order functions for entire holomorphic mappings, classical indicators of orders of growth, and entire functions and varieties of finite order.Chapter 2 is devoted to the appearance of curvature, and Chapter 3 considers the defect relations. The author considers the lemma on the logarithmic derivative, R. Nevanlinna's proof of the defect relation, and refinements of the classical case.

Complex analysis --- Holomorphic mappings --- Applications holomorphes --- 517.53 --- Mappings, Holomorphic --- Functions of several complex variables --- Mappings (Mathematics) --- Functions of a complex variable --- Holomorphic mappings. --- 517.53 Functions of a complex variable --- Fonctions de plusieurs variables complexes --- Fonctions entières --- Functions, Entire --- Algebraic variety. --- Analytic function. --- Analytic set. --- Armand Borel. --- Big O notation. --- Canonical bundle. --- Cartesian coordinate system. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Chern class. --- Compact Riemann surface. --- Compact space. --- Complex analysis. --- Complex manifold. --- Complex projective space. --- Corollary. --- Counting. --- Curvature. --- Degeneracy (mathematics). --- Derivative. --- Differential form. --- Dimension. --- Divisor. --- Elementary proof. --- Entire function. --- Equation. --- Exponential growth. --- Gaussian curvature. --- Hermann Weyl. --- Hodge theory. --- Holomorphic function. --- Hyperplane. --- Hypersurface. --- Infinite product. --- Integral geometry. --- Invariant measure. --- Inverse problem. --- Jacobian matrix and determinant. --- Kähler manifold. --- Line bundle. --- Linear equation. --- Logarithmic derivative. --- Manifold. --- Meromorphic function. --- Modular form. --- Monograph. --- Nevanlinna theory. --- Nonlinear system. --- Phillip Griffiths. --- Picard theorem. --- Polynomial. --- Projective space. --- Q.E.D. --- Quantity. --- Ricci curvature. --- Riemann sphere. --- Scientific notation. --- Several complex variables. --- Special case. --- Stokes' theorem. --- Subset. --- Summation. --- Theorem. --- Theory. --- Uniformization theorem. --- Unit square. --- Volume form. --- Fonctions entières