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Fractal geometry
Editor's note: The following articles by Steven G. Krantz and Benoit B. Mandelbrot have an unusual history. In the fall of 1988, Krantz asked the Bulletin of the American Mathematical Society Book
Invariance Theory Heat Equation and Atiyah Singer Index Theorem
Pseudo-Differential Operators Introduction Fourier Transform and Sobolev Spaces Pseudo-Differential Operators on Rm Pseudo-Differential Operators on Manifolds Index of Fredholm Operators Elliptic
A Primer of Real Analytic Functions
Preface to the Second Edition * Preface to the First Edition * Elementary Properties * Multivariable Calculus of Real Analytic Functions * Classical Topics * Some Questions of Hard Analysis * Results
Function theory of several complex variables
Some integral formulas. Subharmonicity and its applications. Convexity. Hormander's solution of the equation. Solution of the Levi problem and other applications of techniques. Cousin problems,
Function Theory of One Complex Variable
Fundamental concepts Complex line integrals Applications of the Cauchy integral Meromorphic functions and residues The zeros of a holomorphic function Holomorphic functions as geometric mappings
Hp Theory on a Smooth Domain in RN and Elliptic Boundary Value Problems
In this paper, we answer the following two questions. QUESTION 1. Let Ω be an (appropriate) domain inRN. What are the possible (natural) notions of Hp(Ω) that generalize the usual Hardy spaces
Invariant distances and metrics in complex analysis
C onstructing a distance that is invariant under a given class of mappings is one of the fundamental tools for the geometric approach in mathematics. The idea goes back to Klein and even to Riemann.
Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary
A rigidity theorem for holomorphic mappings, in the nature of the uniqueness statement of the classical one-variable Schwarz lemma, is proved at the boundary of a strongly pseudoconvex domain. The
Geometric Integration Theory
Basics.- Caratheodory's Construction and Lower-Dimensional Measures.- Invariant Measures and the Construction of Haar Measure..- Covering Theorems and the Differentiation of Integrals.- Analytical