AVERAGE NUMBER OF REAL ZEROS OF RA NDOM TRIGONOMETRIC POLYNOMIAL
Journal Title: World Journal of Engineering Research and Technology - Year 2017, Vol 3, Issue 3
Abstract
Let EN (T; Φ’, Φ’’) denote the average number of real zeros of the random trigonometric polynomial T=Tn(Φ, ω)=kbaKnKKcos1In the interval (Φ’, Φ’’). Assuming that ak(ω) are independent random variables identically distributed according to the normal law and that bk = kp (p ≥ 0) are positive constants, we show that EN (T: 0, 2π) ~ nOnppnlog2)1(3212212 Outside an exceptional set of measure at most (2/ n) where 222)(log'32124nSSppn β = constant S ~ 1 S’ ~ 1 1991 Mathematics subject classification (amer. Math. Soc.): 60 B 99.
Authors and Affiliations
Dr. P. K. Mishra
Keywords
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