Generalized Householder Transformations

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

Generalized Quantum Integro-Differential Fractional Operator with Application of 2D-Shallow Water Equation in a Complex Domain

In this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic functions, we present a set of integral inequalities using the concepts of subordination and superordination. In addition, as an application, we determine the maximum and minimum solutions of the extended fractional 2D-shallow water equation in a complex domain.

Geometric properties of mixed operator involving Ruscheweyh derivative and Salagean operator

"Operator theory is a magnificent tool for studying the geometric beha- viors of holomorphic functions in the open unit disk. Recently, a combination bet- ween two well known di erential operators, Ruscheweyh derivative and Salagean operator are suggested by Lupas in [10]. In this effort, we shall follow the same principle, to formulate a generalized di erential-difference operator. We deliver a new class of analytic functions containing the generalized operator. Applications are illustrated in the sequel concerning some di erential subordinations of the operator."

Generalized operator for Alexander integral operator

Let Tn be the class of functions f which are defined by a power series f\left( z \right) = z + {a_{n + 1}}{z^{n + 1}} + {a_n}2{z^{n + 2}} + \ldots for every z in the closed unit disc \bar {\mathbb{U}}. With m different boundary points zs, (s = 1,2,...,m), we consider αm ∈ eiβ𝒜−j−λf(𝕌), here 𝒜−j−λ is the generalized Alexander integral operator and 𝕌 is the open unit disc. Applying 𝒜−j−λ, a subclass Bn(αm,β,ρ; j, λ) of Tn is defined with fractional integral for functions f. The object of present paper is to consider some interesting properties of f to be in Bn(αm,β,ρ; j, λ).

Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

Strong Subordination for E -valent Functions Involving the Operator Generalized Srivastava-Attiya

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

The Generalized Operator Based Prony Method

The generalized Prony method is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operator A. However, this procedure requires the evaluation of higher powers of the linear operator A that are often expensive to provide. In this paper we propose two important extensions of the generalized Prony method that essentially simplify the acquisition of the needed samples and, at the same time, can improve the numerical stability of the method. The first extension regards the change of operators from A to $$\varphi (A)$$ φ ( A ) , where $$\varphi $$ φ is a suitable operator-valued mapping, such that A and $$\varphi (A)$$ φ ( A ) possess the same set of eigenfunctions. The goal is now to choose $$\varphi $$ φ such that the powers of $$\varphi (A)$$ φ ( A ) are much simpler to evaluate than the powers of A. The second extension concerns the choice of the sampling functionals. We show how new sets of different sampling functionals $$F_{k}$$ F k can be applied with the goal being to reduce the needed number of powers of the operator A (resp. $$\varphi (A)$$ φ ( A ) ) in the sampling scheme and to simplify the acquisition process for the recovery method.