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p^~=|phi_i(x)><phi_i(t)| (1) p^~sum_(j)c_j|phi_j(t)>=c_i|phi_i(x)> (2) sum_(i)|phi_i(x)><phi_i(x)|=1. (3)

Each of the maps in a chain complex ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->... is known as a boundary operator.

In the notation of Watson (1966), theta=zd/(dz).

An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

Let Omega be a bounded open set in R^d whose boundary partialOmega is at least C^1 smooth and let T:C_c^1(Omega^_)->L^p(partialOmega) (1) be a linear operator defined by ...

The operator tpartial/partialr that can be used to derive multivariate formulas for moments and cumulants from corresponding univariate formulas. For example, to derive the ...

An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

An operator which describes the time evolution of densities in phase space. The operator can be defined by rho_(n+1)=L^~rho_n, where rho_n are the natural invariants after ...

A self-adjoint elliptic differential operator defined somewhat technically as Delta=ddelta+deltad, where d is the exterior derivative and d and delta are adjoint to each ...

The indefinite summation operator Delta^(-1) for discrete variables, is the equivalent of integration for continuous variables. If DeltaY(x)=y(x), then Delta^(-1)y(x)=Y(x).