In this paper, we introduce the generalized Saitoh operator Lp(a, c, η) and using this operator, the new subclasses H n,m(a, c, η), L n,m(a, c, η;μ), H n,m (a, c, η) and L n,m (a, c, η;μ) of the class of multivalent functions denoted by Ap(n) are defined. Further for functions belonging to these classes, certain properties of neighborhoods are studied.

The fusion rules for the vertex operator algebras M(1)+ (of any rank) and V + L (for any positive definite even lattice L) are determined completely.

In this paper, a new monotonicity, M(·, ·)-monotonicity,is introduced in Banach spaces, and the resolvent operator of an M(·, ·)monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·, ·)monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the conver...

We provide the mathematical foundation for the Xm-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional Xm-Jacobi orthogonal polynomials as eigenfunctions. This proves that those polynomials are indeed eigenfunctions of the self-adjoint operator (rather than just formal eigenfunctions). Further, we prove the completenes...

We show that the eigenspaces of the Dirac operator H = α · (D − A(x)) + mβ at the threshold energies ±m are coincide with the direct sum of the zero space and the kernel of the Weyl-Dirac operator σ·(D−A(x)). Based on this result, we describe the asymptotic limits of the eigenfunctions of the Dirac operator corresponding to these threshold energies. Also, we discuss the set of vector potentials...

this research presents a numerical tool to estimate the green's function operator matrix of intraplate faults. having this matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. this information could be employed to predict the location of future powerful earthquakes. to implement fault sliding in fe calculations,...

In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O( √ N/M) for searching an unstructured list of size N with M matches such that 1 ≤ M ≤ N . We will show that the performance of the algorithm is more reliable than known fixed ...

The generalized Funk transform is a integral transform acting from densities on a manifold X to functions defined on a family Σ of hypersurfaces in X. The dual operator M is again a Funk transform which is defined for densities on the manifold Σ. We state twoside estimates for the operator M and a description of the range of the Funk transform operatorM and approximation theorem for the kernel ...

On the Hilbert space ̃L2(T) the singular integral operator with non-Carleman shift and conjugation K = P+ + (aI + AC)P− is considered, where P± are the Cauchy projectors, A = m ∑ j=0 ajU j , a,aj , j = 1,m , are continuous functions on the unit circle T , U is the shift operator and C is the operator of complex conjugation. Some estimates for the dimension of the kernel of the operator K are obt...