عنوان :
قاب هاي تقريبا" دوگان در فضاهاي هيلبرت
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 :
محمدتقي جهانديده
توصيفگر ها :
قاب دوگان , قاب هاي گابر
تاريخ نمايه سازي :
10/4/92
استاد داور :
سيما سلطاني، محمدرضا كوشش
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Approximately Dual Frames in Hilbert Spaces Zahra Maleki zahra maleki@math iut ac ir December 30 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Farid Bahrami fbahrami@cc iut ac ir Advisor Dr Mohammad Taghi Jahandideh jahandid@cc iut ac ir 2010 MSC 42C15 Keywords Frames Dual Frames Approximate Dual Frames Gabor Frames AbstractThis thesis is a generalization of the works done by Christensen and Laugesen 5 We introduceapproximately dual frame in Hilbert spaces Frames were introduced by Du n and Schae er in their fundamental paper They used frames asa tool in the study of nonharmonic Fourier series As the wavelet era began Daubechies Grossmann and Meyer observed that frames can be used to nd series expansions of functions in L2 R that arevery similar to the expansions using orthonormal bases This was the time when many mathematiciansstarted to see the potential of the topic A frame is a sequence of elements fk in H which allows every f H to be written as an k 1in nite linear combination of elements fk in the frame However the corresponding coe cients are notnecessarily unique If fk is a frame then one choice of dual is the canonical dual frame Let fk be a frame k 1 k 1with frame operator S then the frame S 1 fk is called the canonical dual frame of fk k 1 k 1 The frame decomposition stated in f S 1 fk fk f H f k 1is the most important frame result It shows that if fk is a frame for H then every element in H has k 1
استاد راهنما :
فريد بهرامي
استاد مشاور :
محمدتقي جهانديده
استاد داور :
سيما سلطاني، محمدرضا كوشش
