Related papers: Analytic functional calculus for two operators
In this paper, an integral identity for twice differentiable functions is generalized. Then, by using convexity of |f''| or q-th power of |f''| and with the aid of power mean and Holder's inequalities we achieved some new results. We also…
We consider the Lommel functions $s_{\mu,\nu}(z)$ for different values of the parameters $(\mu,\nu)$. We show that if $(\mu,\nu)$ are half integers, then it is possible to describe these functions with an explicit combination of polynomials…
Let $(G,+)$ be a topological abelian group with a neutral element $e$ and let $\mu : G\longrightarrow\mathbb{C}$ be a continuous character of $G$. Let $(\mathcal{H}, \langle \cdot,\cdot \rangle)$ be a complex Hilbert space and let…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
The paper is an investigation of the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of matter relaxation processes in attractive fields. These…
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…
It is shown how to define difference operators and equations on particular lattices $\{x_n\}$, $2n\in\mathbb{Z}$, such that the divided difference operator $(\mathcal{D}f)(x_{n+1/2})= (f(x_{n+1})-f(x_n))/(x_{n+1}-x_n)$ has the property that…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
The general analytic solution to the functional equation $$ \phi_1(x+y)= { { \biggl|\matrix{\phi_2(x)&\phi_2(y)\cr\phi_3(x)&\phi_3(y)\cr}\biggr|} \over { \biggl|\matrix{\phi_4(x)&\phi_4(y)\cr\phi_5(x)&\phi_5(y)\cr}\biggr|} } $$ is…
A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is…
We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an…
Let $\mathcal{A}$ denote the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$ and satisfy the normalization conditions $f(0) = 0$ and $f'(0) = 1$. This paper investigates the inverse logarithmic coefficients…
{Let $N, k$ be positive integers with $k\geq 2$, and $\Omega \subset \mathbb{R}^{N}$ be a domain.} By the well-known properties of the Laplacian and the gradient, we have \[ \Delta(f\cdot g)(x)=g(x) \Delta f(x)+f(x) \Delta g(x)+2\langle…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
In this paper we study the Cauchy problem for diffusion equations associated to a class of strongly hypoelliptic pseudo-differential operators on graded Lie groups. To do so, we develop a global complex functional calculus on graded Lie…
We propose the Lie-algebraic interpretation of poly-analytic functions in $L_2(\C,d\mu)$, with the Gaussian measure $d\mu$, based on a flag structure formed by the representation spaces of the $\mathfrak{sl}(2)$-algebra realized by…
In this paper, we introduce two general subclasses of analytic functions by means of the principle of subordination and investigate the coefficient bounds for functions in theese classes. The well-known results are obtained as a corollary…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
Using three different representations of the bicomplex numbers $T\cong Cl_{C}(1,0) \cong Cl_{C}(0,1)$, which is a commutative ring with zero divisors defined by $T={w_0+w_1 {i_1}+w_2{i_2}+w_3 {j} | w_0,w_1,w_2,w_3 \in{R}}$ where…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…