Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory: Second Edition

The survey of Chebyshev polynomials covers various mathematical areas, with an updated second edition correcting errors and adding new material.

Format: Paperback / softback
Length: 272 pages
Publication date: 30 September 2020
Publisher: Dover Publications Inc.

The Chebyshev polynomials are a fascinating set of mathematical objects that have found applications in a wide range of fields, including interpolation theory, orthogonal polynomials, approximation theory, numerical integration, numerical analysis, and ergodic theory. Originally published in 1974, the text underwent a significant update in 1990, resulting in the second edition. This reprint of the second edition aims to correct various errors and provide new material, including a chapter introducing elementary algebraic and number theoretic properties of Chebyshev polynomials.

Interpolation theory is a fundamental area of mathematics that deals with the construction of functions that pass through a given set of points. Chebyshev polynomials are particularly useful in this context because they can be used to construct polynomials that interpolate a given set of data points with a high degree of accuracy. Orthogonal polynomials are another important area of mathematics that deals with the construction of polynomials that are orthogonal to each other. Chebyshev polynomials are orthogonal with respect to the weight function \(w(x) = \frac{1}{\sqrt{1-x^2}}\), which makes them useful in a variety of applications, including signal processing, image compression, and quantum mechanics. Approximation theory is a branch of mathematics that deals with the approximation of functions by polynomials. Chebyshev polynomials are particularly useful in this context because they can be used to approximate functions with a high degree of accuracy. Numerical integration is a technique used to compute the value of a function over a given interval. Chebyshev polynomials are particularly useful in this context because they can be used to compute the value of a function with a high degree of accuracy. Numerical analysis is a branch of mathematics that deals with the analysis of algorithms and numerical methods. Chebyshev polynomials are particularly useful in this context because they can be used to analyze the behavior of algorithms and numerical methods. Ergodic theory is a branch of mathematics that deals with the study of dynamical systems. Chebyshev polynomials are particularly useful in this context because they can be used to study the behavior of dynamical systems.

The Chebyshev polynomials have several important properties that make them useful in a wide range of applications. One of the most important properties of the Chebyshev polynomials is that they are orthogonal with respect to the weight function \(w(x) = \frac{1}{\sqrt{1-x^2}}\). This property makes them useful in a variety of applications, including signal processing, image compression, and quantum mechanics. Another important property of the Chebyshev polynomials is that they are easy to compute. This property makes them useful in a variety of applications, including numerical integration and numerical analysis.

In addition to their important properties, the Chebyshev polynomials have a number of interesting applications. One of the most interesting applications of the Chebyshev polynomials is in the field of signal processing. Chebyshev polynomials are used to design filters that can be used to remove noise from signals. Chebyshev polynomials are also used to design filters that can be used to compress images. Chebyshev polynomials are also used to design filters that can be used to analyze the behavior of quantum systems.

Another interesting application of the Chebyshev polynomials is in the field of image compression. Chebyshev polynomials are used to design filters that can be used to compress images. Chebyshev polynomials are also used to design filters that can be used to analyze the behavior of quantum systems.

In addition to their applications in signal processing and image compression, the Chebyshev polynomials have a number of other interesting applications. One of the most interesting applications of the Chebyshev polynomials is in the field of quantum mechanics. Chebyshev polynomials are used to design filters that can be used to analyze the behavior of quantum systems. Chebyshev polynomials are also used to design filters that can be used to control quantum systems.

In conclusion, the Chebyshev polynomials are a fascinating set of mathematical objects that have found applications in a wide range of fields, including interpolation theory, orthogonal polynomials, approximation theory, numerical integration, numerical analysis, and ergodic theory. The Chebyshev polynomials have several important properties that make them useful in a wide range of applications, including their orthogonality with respect to the weight function \(w(x) = \frac{1}{\sqrt{1-x^2}}\), their ease of computation, and their interesting applications in signal processing, image compression, and quantum mechanics.

Weight: 392g
Dimension: 152 x 228 x 15 (mm)
ISBN-13: 9780486842332