The Berezin transform $\widetilde{T}$ and the radius of an operator
 $T$ on reproducing kernel Hilbert space $\mathcal{H}\left( Q\right) $
 over some set $Q$ with $K_{\eta}$ are defined,
 respectively, by
 \[
 \widetilde{T}(\eta)=\left\langle {T\frac{K_{\eta}}{{\left\Vert K_{\eta
 }\right\Vert }},\frac{K_{\eta}}{{\left\Vert K_{\eta}\right\Vert }}%
 }\right\ran...

For a compact manifold without boundary a suspended algebra of pseudodifferential operators is considered; it is an algebra of pseudodifferential operators on, and translation-invariant in, an additional real variable. It is shown that the eta invariant, as defined by Atiyah, Patodi and Singer for admissible Dirac operators, extends to a homomorphism from the ring of invertible elements of the ...

In any Banach space a monotone operator with a norm-to-weak upper semicontinuous multivalued selection on an open set D is singlevalued and norm-to-norm upper semicontinuous at the points of a dense G subset of D. Monotone operators | and especially a special case of them, subdiierentials of convex functions | play an important role in various parts of nonlinear analysis. One of the often inves...

We study the transition widths of $\Upsilon(10753)$ and $\Upsilon(11020)$ into standard bottomonium under hypothesis that they correspond to two lowest laying $1^{--}$ hybrid states. employ weakly coupled potential NRQCD an effective filed theory incorporating heavy quark multipole expansions. consider transitions generated by leading order next-to-leading singlet-octet operators. In expansion ...

In the investigation of boundary value problems the construction of a twosided inclusion of the solution can be as important as a numerical approximation of the solution itself. In the present paper we analyze a monotone discretization technique of higher order based upon piecewise interpolation and shifting such that bounding upper and lower solutions are obtained. The monotone discretization ...

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar’s constraint qualification holds. In this paper, we prove the maximal monotonicity of A+B provided that A and B are maximal monotone operators such that domA ∩ int domB ̸= ∅, A+NdomB is of type (FPV), and domA∩domB ⊆ domB. The proof ...

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal monotone operator. This result is then generalized to obtain convergence rates for the problem of finding a common zero of multiple monotone operators by consider...

In any Banach space a monotone operator with a norm-to-weak upper semicontinuous multivalued selection on an open set D is singlevalued and normto-norm upper semicontinuous at the points of a dense Gδ subset of D. Monotone operators — and especially a special case of them, subdifferentials of convex functions — play an important role in various parts of nonlinear analysis. One of the often inve...

In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical re...