Libros de Matemáticas, página 15 de 470

This is the fourth edition of Serge Lang''s Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than in other texts, and the proofs using these methods often shed more light on the results than the standard proofs do. The first part of Complex Analysis is suitable for an introductory course on the undergraduate level, and the additional topics covered in the second part give the instructor of a graduate course a great deal of flexibility in structuring a more advanced course. This is a revised edition, new examples and exercises have been added, and many minor improvements have been made throughout the text.

This unique book is an excellent introduction to the basic properties of wavelets. The fundamental construction of these functions by means of "multiresolution analyses" is presented; in particular, this method is used for introducing the spline wavelets and the compactly supported wavelets. An important feature of this book, however, is the use of the Fourier transform for studying wavelets on the real line. A simple characterization of all wavelets is presented which is most useful for the construction of new families of wavelets. This technique can also be used for obtaining characterizations of low pass filters and scaling functions. Another feature is the use of wavelets for representing those function spaces that are most often encountered in analysis: the Lebesgue spaces, Hardy spaces, and more generally, the Besov spaces, the Sobolev, and the Lipschitz spaces. Other topics, some related to applications, are also included: the Fast Fourier Transform, wavelet packets, frames, local cosine and sine bases and their discrete versions are just some examples. Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: oSeveral bases generated by a single function via translations and dilations oMultiresolution analysis, compactly supported wavelets, and spline wavelets oBand-limited wavelets oUnconditionality of wavelet bases oCharacterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also presen