You are now only searching within the Book Series

is not a valid page number. Please enter a number between 1 and 238

is not a valid page number. Please enter a number between 1 and 238

Page is not a valid page number. Please enter a number between 1 and 238 of 238

Book Series Graduate Texts in Mathematics Volume 1 / 1982 to Volume 286 / 2020

Book Spectral Theory Basic Concepts and Applications

Book Smooth Manifolds and Observables

Book Lectures on Convex Geometry

Book Basic Representation Theory of Algebras

Chapter Differentiation In this chapter we see how to answer this question by considering differentiation issues. We begin by developing a powerful tool called the Hardy–Littlewood maximal inequality. This tool is used to prove an al... Download PDF (498 KB)

Chapter Cutoff and Other Special Smooth Functions on \({\mathbb R}^n\) This is a purely technical chapter, that can be omitted on first reading. It brings together auxiliary statements (in particular, on the existence of cutoff functions) that are used in different places in the ...

Chapter Introduction This chapter gives a brief historical introduction to spectral theory, from Pythagoras to the early 20th century.

Chapter Riemann Integration This brief chapter reviews Riemann integration. Riemann integration uses rectangles to approximate areas under graphs. This chapter begins by carefully presenting the definitions leading to the Riemann integra... Download PDF (384 KB)

Chapter Differential Forms: Classical and Algebraic Approach This chapter deals with differential forms and their applications. It is shown how differential forms can be conceptually redefined and then naturally generalized to become an inherent and very important part ...

Chapter Product Measures Lebesgue measure on R generalizes the notion of the length of an interval. In this chapter, we see how two-dimensional Lebesgue measure on R2 generalizes the notion of the area of a rectangle. More generally, we ... Download PDF (583 KB)

Chapter Linear Maps on Hilbert Spaces A special tool called the adjoint helps provide insight into the behavior of linear maps on Hilbert spaces. This chapter begins with a study of the adjoint and its connection to the null space and range of a l... Download PDF (860 KB)

Chapter Convex Sets Convexity is a basic but fundamental notion in mathematics. A subset of ℝ n \({\mathbb R}^n\) is called convex if for any two of its points, the whole segment connecting these points is contained in...

Chapter Introduction This chapter informally describes the ideology and the motivation of the book. The ideology is that the theory of smooth manifolds and the structures on them can and should be developed starting with the algeb...

Chapter Lp Spaces Important results called Hölder’s inequality and Minkowski’s inequality help us investigate this vector space. Download PDF (489 KB)

Chapter Probability Measures Probability theory has become increasingly important in multiple parts of science. Getting deeply into probability theory requires a full book, not just a chapter. For readers who intend to pursue further stud... Download PDF (517 KB)

Chapter The Operator Relation \(XX^{*}=F(X^{*}X)\) This chapter examines the operator relation \(XX^*=F(X^*X)\) X X ∗ = F ( X ∗ X ) , where F is a Borel function on [0,+ \(\infty \) ∞ ) and X is a densely defined closed operator on a Hilbert space. T...