In fact, the fuzzy Mellin transform is a linear operator in the domain of the strips of convergence.
An encryption system is homomorphic with respect to an operation in the plaintext domain if there exists another operator in the ciphertext domain such that.
This pair of equations are numerically solved for A as an eigenvalue to the operators consisting of the domain operator in Eq. (2.4) and the pair of boundary operators in Eq. (2.9) of Neumann type and ( {H}_z^M 1)={H}_z^D(1) ) of Dirichlet type [4, 17, 32].
We first observe that the denominator of the expression for (C_{H^{-1}}phantom {dot {i}!}) corresponds to the discretization of the Laplacian operator in the frequency domain.
Recallour quadrature operator in the frequency domain X ˆ ϕ = a ˘ ˆ o e i ϕ + a ˘ ˆ o † e − i ϕ written in terms of our gain matrix in (62).
Afterwards, S_MFCC obtained from the signal, ST_MFCC calculated from energy operator in the frequency domain, SW_MFCC from frequency bands of the spectral energy distribution, and SWT_MFCC from combination of all previous are calculated from two signals which are sum of the even and odd IMFs.
Once the optimal correction term (hat{x_e}) is found, the resulting reconstruction is simply computed as (x = tilde{C} tilde{x_0} + hat{x_e})) where (tilde{C}) is a cropping operator in the image domain, mapping images of support (N_2^2) to images of support (N^2).
The present paper gives an abstract method to prove that possibly embedded eigenstates of a self-adjoint operator H lie in the domain of the kth power of a conjugate operator A. Conjugate means here that H and A have a positive commutator locally near the relevant eigenvalue in the sense of Mourre.
The operator (L_{lambda}) is defined in the domain begin{aligned} D(L_{lambda}) =&bigl{ y(x)|y(x),y^{prime }(x), ldots,y^{ m-1)}(x)in operatorname{AC}[a,y^{ m-1 for all }a,bin mathbb{R}, & y(x inll_{lambda}(y)in L_{2}( mathbb{R})bigr}.
The Durrmeyer-type operators in complex domain were recently established in[4, 5, 6, 7, 8, 9, 10, 11, 12], etc. In[13], a Stancu-type generalization of the complex Durrmeyer operator was treated.
