پديد آورنده :
پارسا، طوبي
عنوان :
قاب ها و پايه هاي ريس تعميم يافته
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض، آناليز تابعي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي
يادداشت :
ص.ع:به فارسي و انگليسي
استاد راهنما :
فريد بهرامي
استاد مشاور :
محمود منجگاني
توصيفگر ها :
پايه ي يكا متعامد تعميم يافته
تاريخ نمايه سازي :
25/09/1392
استاد داور :
رسول نصر اصفهاني، محمد رضا كوشش
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتال
چكيده انگليسي :
Abstract In the study of vector spaces one of the most important concepts is that of a basis We require that the elements are linearly independent and very often we even want them to be orthogonal This makes it hard or even impossible to find bases satisfying extra conditions and this is the reason that one might wish to look for a more flexible tool Frames are such tools Frames were first introduced in by Duffin and Schaeffer reintroduced in by Daubechies Grossmann and Meyer and popularized from then on Frames have many nice properties which make them very useful in the characterization of function spaces signal processing and many other fields We refer to for an introduction to frame theory and its applications A sequence of elements in a separable Hilbert space is a frame for H if there exist constants A B such that Let be a frame with frame operator S The frame decomposition for leaves either a frame or an incomplete set is the most important frame result Another result is as follow s The removal of a vector from a frame We define Riesz bases too We see that a Riesz basis for is a frame and a schauder basis for It is seen also that it is equivalent to exact frames Suppose and are two Hilbert spaces and is a sequence of subspaces of where is a subset of is the collection of all bounded linear operators from sequence a generalized frame or simply a g frame for with respect to into We call a if there are two positive constants A and B such that We observe that various generalizations of frames have been proposed recently For example bounded quasi projectors frames of subspaces pseudo frames oblique frames and outer frames All of these generalizations have proved to be useful in many applications Here we point out that they can be regarded as special cases of g frames and many basic properties can be derived within this more general context We define g frame operator and proceed to its features Moreover it is seen how the canonical dual g frames give rise to expansion coefficients with the minimal norm Similar to generalized frames we can define generalized Bessel sequences Riesz bases and orthonormal bases In an important theorem we PDF created with pdfFactory trial version www pdffactory com
استاد راهنما :
فريد بهرامي
استاد مشاور :
محمود منجگاني
استاد داور :
رسول نصر اصفهاني، محمد رضا كوشش
