Introduction to real functions and orthogonal expansions
by Béla Sz.-Nagy.
New York : Oxford University Press, 1965.
xi, 447 págs. : ilustraciones ; 22 cm.
Serie: University texts in the mathematical sciences
Traducción de: Valós függvények és függvénysorok. 1961.
"The book is remarkable for its elegance and clarity. The choice and the ordering of the subjects are very original."—Math. Rev.
Reseña: MathSciNet, 31 #5938
Contenido
- 1. Sets (Some fundamental notions, Point sets)
- 2. Continuous functions (Continuity, Sequences of continuous functions, Approximation of continuous functions by polynomials, Monotonic functions and functions of bounded variation)
- 3. Differentiation (Differentiation of monotonic functions, Dini derivates of arbitrary functions)
- 4. Interval functions; Riemann integral (General theorems and their applications, The Riemann integral, Functions of several variables)
- 5. Lebesgue integral (Definition and fundamental properties, Properties of the integral functions, Measurable functions and sets, Functions of several variables)
- 6. The Stieltjes integral and its generalizations (The Stieltjes integral and linear functionals on continuous functions, Generalizations of the Stieltjes integral, The Lebesgue integral on abstract spaces, The space $L2$, Fourier series, Other orthogonal sequences of functions, Fourier integrals, The $Lp$ spaces)
- 7. Convergence and summability of Fourier series (Historical comments, Some physical problems, Convergence theorems for Fourier series, Summation methods, Summation of Fourier series by the method of arithmetical means, Summation of Fourier series by the Abel-Poisson method).