000 03739nam a22004935i 4500
001 978-3-7643-7605-5
003 DE-He213
005 20160302162512.0
007 cr nn 008mamaa
008 100301s2006 sz | s |||| 0|eng d
020 _a9783764376055
_9978-3-7643-7605-5
024 7 _a10.1007/3-7643-7605-8
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.7
_223
100 1 _aGrigoryan, Suren A.
_eauthor.
245 1 0 _aShift-invariant Uniform Algebras on Groups
_h[electronic resource] /
_cby Suren A. Grigoryan, Thomas V. Tonev.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2006.
300 _aIX, 287 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMonografie Matematyczne, Instytut Matematyczny Polskiel Akademii Nauk (IMPAN) ;
_v68
505 0 _aBanach algebras and uniform algebras -- Three classical families of functions -- Groups and semigroups -- Shift-invariant algebras on compact groups -- Extension of semicharacters and additive weights -- G-disc algebras -- Harmonicity on groups and G-discs -- Shift-invariant algebras and inductive limit algebras on groups.
520 _aShift-invariant algebras are uniform algebras of continuous functions de?ned on compactconnectedgroups,thatareinvariantundershiftsbygroupelements. They areoutgrowths of generalized analytic functions, introduced almost ?fty yearsago by Arens and Singer, and are the central object of this book. Associated algebras of almost periodic functions of real variables and of bounded analytic functions on the unit disc are also considered and carried along within the shift-invariant framework. The adopted general approach leads to non-standard perspectives, never-asked-before questions, and unexpected properties. Thebookisbasedmainlyonourquiterecent,someevenunpublished,results. Most of its basic notions and ideas originate in [T2]. Their further development, however, can be found in journal or preprint form only. Basic terminologyand standard properties of uniform algebrasarepresented in Chapter 1. Associated algebras, such as Bourgain algebras, polynomial ext- sions, and inductive limit algebras are introduced and discussed. At the end of the chapter we present recently found conditions for a mapping between uniform algebras to be an algebraic isomorphism. In Chapter 2 we give fundamentals, v- ious descriptions and standard properties of three classical families of functions – p almost periodic functions of real variables, harmonic functions, andH -functions on the unit circle. Later on, in Chapter 7, we return to some of these families and extend them to arbitrary compact groups. Chapter 3 is a survey of basic prop- ties of topological groups, their characters, dual groups, functions and measures on them. We introduce also the instrumental for the sequel notion of weak and strong hull of a semigroup.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aFunctions of complex variables.
650 0 _aOperator theory.
650 1 4 _aMathematics.
650 2 4 _aFunctional Analysis.
650 2 4 _aFunctions of a Complex Variable.
650 2 4 _aOperator Theory.
700 1 _aTonev, Thomas V.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764376062
830 0 _aMonografie Matematyczne, Instytut Matematyczny Polskiel Akademii Nauk (IMPAN) ;
_v68
856 4 0 _uhttp://dx.doi.org/10.1007/3-7643-7605-8
912 _aZDB-2-SMA
999 _c177361
_d177361