8384

7765

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

هشت،77ص.

ص.ع.به فارسي و انگليسي

فريد بهرامي

محمدتقي جهانديده

15/10/92

سيما سلطاني، محمدرضا كوشش

رياضي

ID7765

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Abstract locally algebras and present many theorems of frames in Hilbert In this thesis we develop the theory of frames in Hilbert modules over modules over locally algebra instead of Hilbert spaces Frames were introduced by Duffin and Schaffer in their fundamental paper They used frames as a tool in the study of nonharmonic fourier series Daubechies Grossmann and Meyer observed that the frames can be used to find series expansions of functions in R that are very similar element in H whitch allows every f to the expansions using orthonormal basis A frame is a sequence of to be written as an countable linear combinations of elements in the frame However the corrospounding coefficients are not necessarily unique General theory of Hilbert modules over an arbitrary algebras was defined by Frank and Larson as a natural generalization of the Hilbert mathematics A Hilbert modules over algebras or locally space theory Theory of Hilbert modules is applied to many field of algebras or locally algebras Inoue have introduced and algebras is equipped with inner product that allowing to take values in studied locally algebras and presented definition and several We will show that if is a frame in Hilbert module X over a unital properties of them locally algebra A then for any x the reconstruction formula x is valid where S is a positive A linear Furthermore we define the unique frame that called bounded adjointable operator on X called frame operator canonical dual frame in Hilbert A module X We proved PDF created with pdfFactory trial version www pdffactory com

فريد بهرامي

محمدتقي جهانديده

سيما سلطاني، محمدرضا كوشش