INDEX 467

equivalent norms, 297interpolation inequality, 300trace, 299

spectral mapping theorem, 437spectral radius, 433spectrum, 429spt, 190square root property, 420

simply connected, 420star center, 361star shaped, 361stereographic projection, 374Stirling’s formula, 138, 268Stone Weierstrass theorem, 87sup

changing order, 28support

function, 259

Tietze extension theorem, 63total variation, 326totally bounded, 48totally ordered, 9, 202translation invariance, 157, 201translations, 416

uniform boundedness, 305uniform boundedness theorem, 305uniform continuity, 55

uniform continuity and compactness, 56uniform convergence

infinite sums, 60uniform norm, 57, 224uniformly bounded, 228uniformly integrable, 179, 186union, 3

variation of constants formula, 411variational inequality, 311vector measures, 325Vitali

convergence theorem, 179Vitali convergence theorem, 181Vitali covering, 204

weak convergence, 323Weierstrass

approximation estimate, 81M test, 16, 61Stone Weierstrass theorem, 83

well ordered sets, 10

Young’s inequality, 342

zeros of analytic functioncounting them, 377

zeta functiondefinition, 371