Functions, spaces, and expansions : mathematical tools in physics and engineering
著者
書誌事項
Functions, spaces, and expansions : mathematical tools in physics and engineering
（Applied and numerical harmonic analysis / series editor, John J. Benedetto）
Birkhäuser, c2010
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering.
Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.
目次
Mathematical Background.- Normed Vector Spaces.- Banach Spaces.- Hilbert Spaces.- The Lp-spaces.- The Hilbert Space L2.- The Fourier Transform.- An Introduction to Wavelet Analysis.- A Closer Look at Multiresolution Analysis.- B-splines.- Special Functions.- Appendix A.- Appendix B.
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