Resolvent set of the M/MB/1 operator

Resolvent Estimates of the Dirac Operator

Hermitian Geometry on Resolvent Set

For a tuple A = (A1, A2, ..., An) of elements in a unital Banach algebra B, its projective joint spectrum P (A) is the collection of z ∈ C such that A(z) = z1A1 +z2A2 + · · ·+znAn is not invertible. It is known that the B-valued 1-form ωA(z) = A−1(z)dA(z) contains much topological information about the joint resolvent set P (A). This paper defines Hermitian metric on P (A) through the B-valued ...

Non-Perturbative Dirac Operator Resolvent Analysis

We analyze the 1 + 1 dimensional Nambu-Jona-Lasinio model nonperturbatively. In addition to its simple ground state saddle points, the effective action of this model has a rich collection of non-trivial saddle points in which the composite fields σ(x) = 〈ψ̄ψ〉 and π(x) = 〈ψ̄iγ5ψ〉 form static space dependent configurations because of non-trivial dynamics. These configurations may be viewed as one d...

Resolvent Operator Method for General Variational Inclusions

In this paper, we introduce a new class of variational inclusions involving three operator. Using the resolvent operator technique, we establish the equivalence between the general variational inclusions and the resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving the general variational inclusions. We also consider the cr...

The resolvent trace of an elliptic cone operator

This note discusses some aspects of the analysis leading to the proof of the main theorem in [10] (stated here as Theorem 1) on the structure of the asymptotics of the resolvent trace of a general elliptic cone operator as the spectral parameter tends to infinity, under suitable minimal growth assumptions on the principal symbols of the operator. We deal with an elliptic cone differential operator