A Course in Abstract Harmonic Analysis by Gerald B. Folland PDF

By Gerald B. Folland

ISBN-10: 0849384907

ISBN-13: 9780849384905

Summary idea continues to be an crucial beginning for the examine of concrete instances. It exhibits what the final photograph should still seem like and offers effects which are important repeatedly. regardless of this, besides the fact that, there are few, if any introductory texts that current a unified photo of the final summary theory.A direction in summary Harmonic research deals a concise, readable creation to Fourier research on teams and unitary illustration conception. After a quick assessment of the correct components of Banach algebra idea and spectral concept, the e-book proceeds to the elemental proof approximately in the community compact teams, Haar degree, and unitary representations, together with the Gelfand-Raikov lifestyles theorem. the writer devotes chapters to research on Abelian teams and compact teams, then explores brought about representations, that includes the imprimitivity theorem and its purposes. The publication concludes with an off-the-cuff dialogue of a few extra facets of the illustration thought of non-compact, non-Abelian teams.

Show description

Read Online or Download A Course in Abstract Harmonic Analysis PDF

Best functional analysis books

Ethan D. Bloch's The Real Numbers and Real Analysis PDF

This article is a rigorous, exact creation to genuine research that provides the basics with transparent exposition and punctiliously written definitions, theorems, and proofs. the alternative of fabric and the versatile association, together with 3 assorted entryways into the research of the true numbers, making it both acceptable to undergraduate arithmetic majors who are looking to proceed in arithmetic, and to destiny arithmetic academics who are looking to comprehend the speculation at the back of calculus.

Paul M. Gauthier (auth.)'s Lectures on Several Complex Variables PDF

​​​This monograph presents a concise, available picture of key issues in numerous advanced variables, together with the Cauchy critical formulation, sequences of holomorphic features, plurisubharmonic services, the Dirichlet challenge, and meromorphic features. in keeping with a direction given at Université de Montréal, this short creation covers parts of up to date value that aren't pointed out in so much remedies of the topic, corresponding to modular varieties, that are crucial for Wiles' theorem and the unification of quantum conception and common relativity.

Applied Functional Analysis by J. Tinsley Oden PDF

Via a number of illustrative examples and reviews, utilized sensible research, moment version demonstrates the rigor of common sense and systematic, mathematical considering. It offers the mathematical foundations that result in classical leads to useful research. extra particularly, the textual content prepares scholars to profit the variational conception of partial differential equations, distributions and Sobolev areas, and numerical research with an emphasis on finite aspect equipment.

Richard L. Wheeden's Measure and integral : an introduction to real analysis PDF

Now thought of a vintage textual content at the subject, degree and indispensable: An advent to genuine research presents an advent to genuine research by means of first constructing the speculation of degree and integration within the uncomplicated environment of Euclidean house, after which providing a extra basic remedy in keeping with summary notions characterised via axioms and with much less geometric content material.

Additional info for A Course in Abstract Harmonic Analysis

Example text

P. Smith, Testing Schatten class Hankel operators and Carleson embeddings via reproducing kernels, J. Lond. Math. Soc. 71 (2005) 172–186. [35] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, New Jersey, 1970. [36] M. Stoll, A characterization of Hardy spaces on the unit ball of Cn , J. Lond. Math. Soc. 48 (1993) 126–136. [37] Z. Wu, A new characterization for Carleson measures and some applications, Integral Equations Operator Theory 71 (2011) 161–180.

Math. Soc. 140 (2012) 4247–4257. [15] P. Duren, Extension of a theorem of Carleson, Bull. Amer. Math. Soc. 75 (1969) 143–146. [16] C. Fefferman, E. Stein, H p spaces of several variables, Acta Math. 129 (1972) 137–193. [17] J. Garnett, R. Latter, The atomic decomposition for Hardy spaces in several complex variables, Duke Math. J. 45 (1978) 815–845. [18] M. Gowda, Nonfactorization theorems in weighted Bergman and Hardy spaces on the unit ball of Cn , Trans. Amer. Math. Soc. 277 (1983) 203–212. [19] L.

Bn Putting all together and taking into account that Kzt (1 − |z|2 )−(n+1) , we have that T is in Sp if and only if T p kzt , kzt H2 2 2 2t−1 H 2 (1 − |z| ) is comparable to dλn (z) < ∞. 31]) T p kzt , kzt H2 ≤ T kzt , kzt p H2 = [T t (z)]p , 0 0 and consider the function Ft (z) = T kzt H . If p ≥ 2 and T is in Sp then Ft ∈ Lp (Bn , dλn ).

Download PDF sample

A Course in Abstract Harmonic Analysis by Gerald B. Folland

by Kevin

Rated 4.46 of 5 – based on 47 votes