6485

6050

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1390

[هشت]، 106ص.: مصور

ص.ع. به فارسي و انگليسي

محمد تقي جهانديده

عبدالكريم هدايتيان

26/11/90

فريد بهرامي، رسول نصر اصفهاني

1396/10/12

كتابنامه

علوم رياضي

رياضي

ID6050

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Subnormality and Moment Problems Amjad Salari a salari@math iut ac ir November 2011 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr M Taghi Jahandide Jahandid@cc iut irAdvisor Dr A Karim Hedayatian hedayati@shirazu ac ir2000 MSC 47B15 47B20 44A60 47A20 13B30 Key words Bounded and unbounded sub normal operators spectral measure moment problems algebraicset algebras of fractions Abstract Paul R Halmos introduced the concept of subnormality in 1950 at the same time thathe introduced hyponormality Both of these concepts were inspired by the unilateral shift perhaps the best understood non normal operator The unilateral shift was the dominantexample of a subnormal operator for twenty ve years on the other hand there exists a strong connection between operator theory specialsubnormal operators and the moment problem They interact very often sometimes in asubtle unexpected way It is possible to use a subnormality result used to solve a momentproblem Conversely there are situations when the solution to a moment problem leads tothe existence of a normal extension for some operators the present work endeavor to presentseveral results sustaining the interplay mentioned above as well as the necessary backgroundto understand those phenomena both is a bounded or an unbounded context In special case a moment problem is give by following Let I R be an interval For apositive measure on I the nth moment is de ned by I xn d provided the integral exists If sn n 0 is a sequence of real numbers the moment problem on I consists of solving thefollowing three problems I Dose there exist a positive measure on I with moments sn n 0 In the a rmative II is this positive measure uniquely determined by the moments sn n 0 If not III how can one describe all positive measures on I with moments sn n 0 Without loss of generality we may always assume that s0 1 This is just a question ofnormalizing the involved measures to be probability measures When is a positive measure with moments sn n 0 we say that is a solution to themoment problem If the solution of moment problem is unique the moment problem is calleddeterminate Otherwise the moment problem is side to be indeterminate We know there are three essentially di erent types of closed intervals For historicalreasons the moment problem on 0 is called the Stieltejes moment problems the momentproblem on R is called Hamburger moment problem and the moment problem on 0 1 isreferred to as the Hausdorf f moment problem In chapter one we give a history of subnormal operators and moment problems In chaptertwo and three we give a brief review of measure theory operator theory and normal operators In chapter four we give an explicit solution to the scalar moment problem on semi algebraiccompact subsets of Rn and apply this result to the study of some operator multi sequences In 1

محمد تقي جهانديده

عبدالكريم هدايتيان

فريد بهرامي، رسول نصر اصفهاني