11523

10586

كارشناسي ارشد

آناليز تابعي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

هشت، 78ص.

فريد بهرامي

علي رجالي

محمود منجگاني، محمدرضا كوشش

1395/07/18

رياضي

ID10586

A Variational Principle in the Dual Pair of Reproducing Kernel Hilbert Spaces Azadeh Ha zi a ha zi@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Farid Bahrami fbahrami@cc iut ac ir Advisor Dr Ali Rejali a rejali@cc iut ac ir 2010 MSC 60k35 46E22 Keywords Reproducing Kernel Hilbert Space Determinental point process Gibbs measure Abstract In this thesis we will consider certain variational principle arising in the dual pair of reproducingkernel Hilbert spaces abbreviated by RKH space hereafter We nd an application for showing theGibbsianness of some determinantal point processes in short DPP s in discrete spaces Determinantal point processes or fermion random point elds are probability measures on thecon guration space of say particles The particles may move on the continuum spaces or on thediscrete spaces In the thesis we will focus on the DPP s on the discrete sets The basics of DPP sincluding their de nitions and basic properties can be found in several papers Let E be any countable set e g E Zd the d dimensional lattice space and H0 l2 E bethe Hilbert space of square summable functions sequences on E Let A be a bounded and positivede nite operator on H0 and A x y x y E be the matrix elements of A w r t the usual basis ofH0 We consider a reproducing kernel Hilbert space H with a reproducing kernel A x y Wheneverthere is a zero in the spectrum of A then A is not invertible so we impose a suitable condition onA to get another matrix B which is roughly the representation of A 1 for which A 1 may be anunbounded operator We also consider another reprouducig kernel Hilbert space H with a kernelfunction B x y so that H H0 H

فريد بهرامي

علي رجالي

محمود منجگاني، محمدرضا كوشش