پديد آورنده :
حسين آبادي، جواد
عنوان :
ساخت قاب ها براي فضاهاي هيلبرت با بعد متناهي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
فريد بهرامي
استاد مشاور :
محمدرضا كوشش
توصيفگر ها :
تجزيه مقدار تكين , عملگر تركيب﴿پيش قابي﴾ , احاطه سازي , پتانسيل قاب
تاريخ نمايه سازي :
10/4/92
استاد داور :
محمد تقي جهانديده، مهدي نعمتي
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Constructing frames for nite dimensional Hilbert spaces Javad Hosainabadi j hosainabadi@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Farid Bahrami fbahrami@cc iut ac ir Advisor Dr Mohammad Reza Koushesh koushesh@cc iut ac ir 2000 MSC 42C15 46C05 Keywords Frames Finite dimensional Hilbert spaces Synthesis operator Singular value decomposition Majorization Frame potential Abstract In this thesis we construct frames for nite dimensional Hilbert spaces H N This approach allowsfor the construction of frames with prescribed properties Here F denots either the scaler eld R or C Let N N and M N In the case M N FMdenotes Euclidean space and if M FM denotes the space of square summable sequences l2 First we construct frames for nite dimensional Hilbert spaces using decomposition of the synthesisoperator F via singular value decomposition SVD which is stated in the following theorem Theorem Let N N and M N Let fn M be a Bessel sequence in H N with Bessel operator n 1F FM H N which has a matrix representation F f1 fM with an SVD or a reduced SVDgiven by F U V Then the sequence fn M is a frame for H N if and only if the singular values n 1 1 N of F are N positive real numbers Furthermore fn M is a tight frame if and only if n 1 the singular value i for all i 1 N Second using the singular values and corresponding singular vectors of the synthesis operator weconstruct frames with prescribed norms for the frame vectors by theory of Majorization Here we givenecessary and su cient conditions to construct nite element frames for nite dimensional Hilbertspaces as stated in the following theorem Theorem Let N M a1 aM 0 and 1 N 0 Then the following are equivalent
استاد راهنما :
فريد بهرامي
استاد مشاور :
محمدرضا كوشش
استاد داور :
محمد تقي جهانديده، مهدي نعمتي
