let  be a hilbert space of functions analytic on a plane domain  such that for every  in  the functional of evaluation at  is bounded. assume further that  contains the constants and admits multiplication by the independent variable , , as a bounded operator. we give sufficient conditions for  to be reflexive for all positive integers .

INVARIANT SUBSPACES OF ABSTRACT MULTIPLICATION OPERATORS by Hermann Flaschka We describe a class of operators on a Banach space ft whose members behave, in a sense, like multiplication operators, and consequently leave invariant a proper closed subspace of IB. One of the sufficient conditions for an operator to be such an "abstract multiplication" bears a striking resemblence to an assumption m...

This paper presents integer multiplication and division operators dedicated to Virtex-II FPGAs from Xilinx. Those operators are based on small 18×18 multiplier blocks available in the Virtex-II device family. Various trade-offs are explored (computation decomposition, radix, digit sets . . . ) using specific VHDL generators. The obtained operators lead to speed improvements up to 18% for multip...

A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one. The multiplication rules of the octonions define the multiplication rules of the corresponding operators with quantum corrections. The self-consistency of the operator algebra is proved for the product of three operators. Some properties of the non-associative quantum mec...

We consider a quantum test particle in the background of a Newtonian gravitational field in the framework of Cartan’s formulation of nonrelativistic spacetime. We have proposed a novel quantization of a point particle which amounts to introducing its position operators as multiplication with the corresponding Riemann normal coordinates and momentum operators as infinitesimal right translation o...

An operator family of densely defined closed linear operators and the multiplication operator associated with it are considered. The spectrum of this multiplication operator is expressed in terms of the spectra of the operators in the given family. Mathematics Subject Classification (2000). Primary 47A10; Secondary 47A56, 47B40, 47E05, 76B99.

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work [5, 6] we gave many decidability as well as undecidability results for multiple equational theories, involving various properties o...