17 citations · 36 across the 6 of their papers we have counts for
6 papers
Some spectral properties of Rooms and Passages domains and their skeletons
B. M. Brown, W. D. Evans, I. G. Wood
In this paper we investigate spectral properties of Lapla- cians on Rooms and Passages domains. In the first part, we use Dirichlet- Neumann bracketing techniques to show that for…
The Dirac-Hardy and Dirac-Sobolev inequalities in
A. A. Balinsky, W. D. Evans, T. Umeda
Dirac-Sobolev and Dirac-Hardy inequalities in are established in which the spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak $L^…
Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators
A. Balinsky, W. D. Evans, Y. Saito
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where is -matrix-valued and of orde…
Improved Hardy-Sobolev inequalities
A. Balinsky, W. D. Evans, D. Hundertmark +1
The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent impr…
Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum
W. D. Evans, M. Solomyak
In the model suggested by Smilansky one studies an operator describing the interaction between a quantum graph and a system of one-dimensional oscillators attached at several d…
The Askey-Wilson polynomials and q-Sturm-Lioville problems
B. Malcolm Brown, William Desmond Evans, Mourad E. H. Ismail
We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L^2(-1,1,(1-x^2)^-1/2 dx) defined as a Cauchy principle value and show that…