Results 11 to 20 of about 64 (33)

Meromorphic function fields closed by partial derivatives

, 2019
We characterize meromorphic function fields closed by partial derivatives in n ...
Abe, Yukitaka
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Solution of systems of partial differential equations by using properties of monogenic functions on commutative algebras [PDF]

, 2018
Some systems of differential equations with partial derivatives are studied by using the properties of Gateaux differentiable functions on commutative algebras.
Kolomiiets, T., Pogorui, A., Rodriguez-Dagnino, R.M.   +2 more
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Solutions of several general quadratic partial differential-difference equations in ℂ2

Demonstratio Mathematica
In this article, we have introduced general transformation to solving the general quadratic equations. It is of interest to know about the existence and form of the solutions of general quadratic functional equations.
Ahamed Molla Basir, Mandal Sanju
doaj   +1 more source

WKB eigenmode construction for analytic Toeplitz operators

, 2022
We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of non-degenerate wells. These almost eigenfunctions follow the WKB ansatz; the error is O(exp(--cN)), where c > 0 and N $\rightarrow$ +$\infty$ is the ...
Deleporte, Alix
core  

Split quaternion Fourier transforms for two-dimensional real invariant field

Demonstratio Mathematica
The article gives the corresponding split quaternions in Clifford analysis and the split Fourier transform (FT). Also, we investigate some properties of the split FT and apply to generalizations of the quaternion FT.
Kim Ji Eun
doaj   +1 more source

Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$ [PDF]

, 2011
We construct an example of a smooth map $\mathbb{C}\to\mathbb{C}^2$ which vanishes to infinite order at the origin, and such that the ratio of the norm of the $\bar z$ derivative to the norm of the $z$ derivative also vanishes to infinite order.
Coffman, Adam, Pan, Yifei
core   +3 more sources

Degenerating Hermitian metrics and spectral geometry of the canonical bundle

, 2018
Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $m$. In this paper we are interested in the Dolbeault operator acting on the space of $L^2$ sections of the canonical bundle of $reg(X)$, the regular part of $X$.
Bei, Francesco
core   +1 more source

Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras [PDF]

, 2013
It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper, we extend this idea to finite-dimensional commutative algebras; that is, we prove that if some basis of a subspace of ...
Pogoruі, А. А., Rodríguez-Dagnіno, Ramón М., Shapіro, Мichael   +2 more
core  

On the Laplace-Beltrami operator on compact complex spaces

, 2019
Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $v>1$. In this paper we show that the Friedrichs extension of both the Laplace-Beltrami operator and the Hodge-Kodaira Laplacian acting on functions has discrete ...
Bei, Francesco
core   +1 more source

Characterizations of transcendental entire solutions of trinomial partial differential-difference equations in ℂ2#

Demonstratio Mathematica
This study is devoted to exploring the existence and the precise form of finite-order transcendental entire solutions of second-order trinomial partial differential-difference equations L(f)2+2hL(f)f(z1+c1,z2+c2)+f(z1+c1,z2+c2)2=eg(z1,z2)L{(f)}^{2}+2hL(f)
Xu Hong Yan, Haldar Goutam
doaj   +1 more source