10090

9320

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

هشت، 70ص.: مصور

ص.ع. به فارسي و انگليسي

1396/09/27

كتابنامه

علوم رياضي

رياضي

ID9320

Orthogonality from disjoint support in reproducing kernel Hilbert spaces Mohammad Reza Javadi mr javadi@math iut ac ir 2014 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 46E22 Keywords Orthogonality Reproducing kernel Hilbert space Reproducing kernel Feature map Translation invariant kernels Sobolev spaces AbstractAssume H is a Hilbert space of scalar valued functions on a set X If for each x X the linearfunctional x H F de ned by x f f x for each f in the space H is a continuous linearfunctional then H is called a reproducing kernel Hilbert space or simply a RKHS Let C X denote the set of all the continuous functions on a certain topological space X The supportof a function f C X denoted by supp f is the closure in X of the subset f x X f x 0 Suppose we have a Hilbert space H all of whose elements are continuous functions on X We saythat disjoint support implies orthogonality in H if for all f g H satisfying supp f supp g there holds f g H 0 where H denotes the inner product on H If disjoint support impliesorthogonality in H we also say that H has the orthogonality from disjoint support property Let H be an RKHS on a topological space X By the Riesz representation theorem applied to thecontinuous linear functional x for every x X there exists a unique function K X X C suchthatK x H for all x X andf x f K x H for all x X and f H 1 The function Kx is called the reproducing kernel for the point x The two variable function de ned

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