On the Distribution of Eigenvalues of Kernels and Matrices |
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2a chos application arbitrarily assertion choose clearly illustrates columns common divisor conclude Theorem concludes the proof Consider contains a proof Cornell University determinants diagonal DISTRIBUTION OF EIGENVALUES double roots dudv eigenvector belonging eigenvector equation exp ln felē finite Fn,h function Graduate Hence ia(n+k independent integral equation interval a,b k2ri kernel last k rows math matrix monotone multiplicity non zero elements Notice obtain open interval pair of roots pl-k patak-1 plak polynomial positive limit point positive root Professor Mark Kac proof of Theorem proves the lemma purely imaginary real or purely replacing satisfied sequence Similarly subscripts sufficiently large sufficiently small Theorem III Thesis QA total zero trace unit circle values Walter Lynn Murdock zero elements ΕΠ მგ მგ