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A development of some of the principal applications of function
theory in several complex variables to Banach algebras. The authors
do not presuppose any knowledge of several complex variables on the
part of the reader, and all relevant material is developed within
the text. Furthermore, the book deals with problems of uniform
approximation on compact subsets of the space of n complex
variables. This third edition contains new material on maximum
modulus algebras and subharmonicity, the hull of a smooth curve,
integral kernels, perturbations of the Stone-Weierstrass Theorem,
boundaries of analytic varieties, polynomial hulls of sets over the
circle, areas, and the topology of hulls. The authors have also
included a new chapter commenting on history and recent
developments, as well as an updated and expanded reading list.
A development of some of the principal applications of function
theory in several complex variables to Banach algebras. The authors
do not presuppose any knowledge of several complex variables on the
part of the reader, and all relevant material is developed within
the text. Furthermore, the book deals with problems of uniform
approximation on compact subsets of the space of n complex
variables. This third edition contains new material on maximum
modulus algebras and subharmonicity, the hull of a smooth curve,
integral kernels, perturbations of the Stone-Weierstrass Theorem,
boundaries of analytic varieties, polynomial hulls of sets over the
circle, areas, and the topology of hulls. The authors have also
included a new chapter commenting on history and recent
developments, as well as an updated and expanded reading list.
This book introduces the concepts of linear algebra through the
careful study of two and three-dimensional Euclidean geometry. This
approach makes it possible to start with vectors, linear
transformations, and matrices in the context of familiar plane
geometry and to move directly to topics such as dot products,
determinants, eigenvalues, and quadratic forms. The later chapters
deal with n-dimensional Euclidean space and other
finite-dimensional vector space.
Linear Algebra Through Geometry introduces the concepts of linear
algebra through the careful study of two and three-dimensional
Euclidean geometry. This approach makes it possible to start with
vectors, linear transformations, and matrices in the context of
familiar plane geometry and to move directly to topics such as dot
products, determinants, eigenvalues, and quadratic forms. The later
chapters deal with n-dimensional Euclidean space and other
finite-dimensional vector space. Topics include systems of linear
equations in n variable, inner products, symmetric matrices, and
quadratic forms. The final chapter treats application of linear
algebra to differential systems, least square approximations and
curvature of surfaces in three spaces. The only prerequisite for
reading this book (with the exception of one section on systems of
differential equations) are high school geometry, algebra, and
introductory trigonometry.
Eidgenossische Technische Hochschule. Zurich, Forschungsinstitut
fur Mathematik. Wintersemester 1963/64"
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