Bilinear phase‐plane distribution functions and positivity
نویسندگان
چکیده
منابع مشابه
Positivity of Time-frequency Distribution Functions
This paper deals with the question how various lInaturalll conditions posed on time-frequency distribution functions prevent them to be non-negative everywhere for all signals. The attention is mainly restricted to distribution functions that involve the signal bilinearly. This paper summarizes and extends results recently obtained; the emphasis is on a coherent presentation of these results, r...
متن کاملPositivity bounds on spin-one distribution and fragmentation functions
We establish a connection between the distribution functions of quarks in spin-one hadrons and the helicity matrix for forward scattering of antiquarks off spin-one hadrons. From positivity of this matrix we obtain inequality relations among the distribution functions. Analogous relations hold also for fragmentation functions. The bounds we obtained can be used to constrain estimates of unknown...
متن کاملSome bilinear generating functions.
In the present paper, the author applies some of his earlier results which extend the well-known Hille-Hardy formula for the Laguerre polynomials to certain classes of generalized hypergeometric polynomials in order to derive various generalizations of a bilinear generating function for the Jacobi polynomials proved recently by Carlitz. The corresponding results for the polynomials of Legendre,...
متن کاملThe Bilinear Maximal Functions
The bilinear maximal operator defined below maps L × L into L provided 1 < p, q <∞, 1/p+ 1/q = 1/r and 2/3 < r ≤ 1. Mfg(x) = sup t>0 1 2t ∫ t −t |f(x+ y)g(x− y)| dy In particular Mfg is integrable if f and, g are square integrable, answering a conjecture posed by Alberto Calderón. 1 Principal Results In 1964 Alberto Calderón defined a family of maximal operators by Mfg(x) = sup t>0 1 2t ∫ t −t ...
متن کاملBilinear Sums with Exponential Functions
Let g = 0,±1 be a fixed integer. Given two sequences of complex numbers (φm) ∞ m=1 and (ψn) ∞ n=1 and two sufficiently large integers M and N , we estimate the exponential sums ∑ p≤M gcd(ag,p)=1 ∑ 1≤n≤N φpψnep (ag ) , a ∈ Z, where the outer summation is taken over all primes p ≤ M with gcd(ag, p) = 1.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1985
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.526868