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Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

f(I) is the collection of all real-valued continuous functions defined on some interval I. f^((n))(I) is the collection of all functions in f(I) with continuous nth ...

Gives a lower bound for the inner product (Lu,u), where L is a linear elliptic real differential operator of order m, and u has compact support.

A vector norm defined for a vector x=[x_1; x_2; |; x_n], with complex entries by |x|_infty=max_(i)|x_i|. The vector norm |x|_infty of the vector x is implemented in the ...

A vector norm defined for a vector x=[x_1; x_2; |; x_n], with complex entries by |x|_1=sum_(r=1)^n|x_r|. The L^1-norm |x|_1 of a vector x is implemented in the Wolfram ...

Whittaker and Watson (1990, pp. 539-540) write Lamé's differential equation for ellipsoidal harmonics of the first kind of the four types as ...

Suppose that {f_n} is a sequence of measurable functions, that f_n->f pointwise almost everywhere as n->infty, and that |f_n|<=g for all n, where g is integrable. Then f is ...

The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.

An elliptic function with no poles in a fundamental cell is a constant.