Three Term Weighted Type Fractional Fourier Transform Based Generalized Hybrid Carrier and Its Application into PAPR Suppression

To suppress the peak to average power ratio (PAPR) of wireless communication based upon multi-carrier system. We, in this paper, proposed the three term weighted type fractional Fourier transform (3-WFRFT) based generalized hybrid carrier (GHC) system. We first provide the definition of 3-WFRFT. Moreover, some useful properties of 3-WFRFT have been presented, in this paper, which will helpful to comprehend the novel 3-WFRFT transform. Furthermore, we take PAPR of the proposed algorithm, in comparison with orthogonal frequency division multiplexing (OFDM) system and single carrier modulation (SC) system under typical complementary cumulative density function (CCDF) level. It would be demonstrated that, from some numerical simulations, the proposed 3-WFRFT based GHC performs better than OFDM system and will be useful to reduce the PAPR level.

Some Double Generalized Weighted Fractional Integral Inequalities Associated with Monotone Chebyshev Functionals

In this manuscript, we study the unified integrals recently defined by Rahman et al. and present some new double generalized weighted type fractional integral inequalities associated with increasing, positive, monotone and measurable function F. Also, we establish some new double-weighted inequalities, which are particular cases of the main result and are represented by corollaries. These inequalities are further refinement of all other inequalities associated with increasing, positive, monotone and measurable function existing in literature. The existing inequalities associated with increasing, positive, monotone and measurable function are also restored by applying specific conditions as given in Remarks. Many other types of fractional integral inequalities can be obtained by applying certain conditions on F and Ψ given in the literature.

More General Weighted-Type Fractional Integral Inequalities via Chebyshev Functionals

The purpose of this research paper is first to propose the generalized weighted-type fractional integrals. Then, we investigate some novel inequalities for a class of differentiable functions related to Chebyshev’s functionals by utilizing the proposed modified weighted-type fractional integral incorporating another function in the kernel F(θ). For the weighted and extended Chebyshev’s functionals, we also propose weighted fractional integral inequalities. With specific choices of ϖ(θ) and F(θ) as stated in the literature, one may easily study certain new inequalities involving all other types of weighted fractional integrals related to Chebyshev’s functionals. Furthermore, the inequalities for all other type of fractional integrals associated with Chebyshev’s functionals with certain choices of ϖ(θ) and F(θ) are covered from the obtained generalized weighted-type fractional integral inequalities.

Multiweighted-Type Fractional Fourier Transform: Unitarity

The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform as basic functions to prove and discuss the unitarity. Thanks to the growing body of research, we found that the effective weighting term of the M-WFRFT is only four terms, none of which are extended to M terms, as described in the definition. Furthermore, the program code is analyzed, and the result shows that the previous work (Digit Signal Process 2020: 104: 18) based on MATLAB for unitary verification is inaccurate.

Key Validity Using the Multiple-Parameter Fractional Fourier Transform for Image Encryption

As a symmetric encryption algorithm, multiple-parameter fractional Fourier transform (MPFRFT) is proposed and applied to image encryption. The MPFRFT with two vector parameters has better security, which becomes the main technical means to protect information security. However, our study found that many keys of the MPFRFT are invalid, which greatly reduces its security. In this paper, we propose a new reformulation of MPFRFT and analyze it using eigen-decomposition-type fractional Fourier transform (FRFT) and weighted-type FRFT as basis functions, respectively. The results show that the effective keys are extremely limited. Furthermore, we analyze the extended encryption methods based on MPFRFT, which also have the security risk of key invalidation. Theoretical analysis and numerical simulation verify our point of view. Our discovery has important reference value for a class of generalized FRFT image encryption methods.

New characterizations for differences of composition operators between weighted-type spaces in the unit ball

In this paper, we present some asymptotically equivalent expressions to the essential norm of differences of composition operators acting on weighted-type spaces of holomorphic functions in the unit ball of . Especially, the descriptions in terms of are described. From which the sufficient and necessary conditions of compactness follows immediately. Also, we characterize the boundedness of these operators.

The Product-Type Operators from Hardy Spaces into n th Weighted-Type Spaces

The main goal of this paper is to investigate the boundedness and essential norm of a class of product-type operators T u , v , φ m , m ∈ ℕ from Hardy spaces into n th weighted-type spaces. As a corollary, we obtain some equivalent conditions for compactness of such operators.

Linear Differential Equations on Some Classes of Weighted Function Spaces

Some weighted-type classes of holomorphic function spaces were introduced in the current study. Moreover, as an application of the new defined classes, the specific growth of certain entire-solutions of a linear-type differential equation by the use of concerned coefficients of certain analytic-type functions, that is the equation h(k)+Kk−1(υ)h(k−1)+…+K1(υ)h′+K0(υ)h=0, will be discussed in this current research, whereas the considered coefficients K0(υ),…,Kk−1(υ) are holomorphic in the disc ΓR={υ∈C:|υ|<R},0<R≤∞. In addition, some non-trivial specific examples are illustrated to clear the roles of the obtained results with some sharpness sense. Hence, the obtained results are strengthen to some previous interesting results from the literature.