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The mathematical study of the scattering operator and Schrödinger equation.

Given a subalgebra A of the algebra B(H) of bounded linear transformations from a Hilbert space H onto itself, the vector v in H is a separating vector for A if the only ...

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...

A polynomial sequence p_n(x) is called the basic polynomial sequence for a delta operator Q if 1. p_0(x)=1, 2. p_n(0)=0 for all n>0, 3. Qp_n(x)=np_(n-1)(x). If p_n(x) is a ...

The finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special ...

A square matrix A is a normal matrix if [A,A^(H)]=AA^(H)-A^(H)A=0, where [a,b] is the commutator and A^(H) denotes the conjugate transpose. For example, the matrix [i 0; 0 ...

Let a divisor d of n be called a 1-ary (or unitary) divisor if d_|_n/d (i.e., d is relatively prime to n/d). Then d is called a k-ary divisor of n, written d|_kn, if the ...

For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

Calabi-Yau spaces are important in string theory, where one model posits the geometry of the universe to consist of a ten-dimensional space of the form M×V, where M is a four ...