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Monogenic functions with values in algebras of the second rank over the complex field and a generalized biharmonic equation with a triple characteristic
The statement that any two-dimensional algebra 𝔹 * of the second rank with unity over the field of complex numbers contains such a basis { e 1 ; e 2 }...
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Monogenic Functions in Commutative Algebras Associated with Classical Equations of Mathematical Physics
The methods involving the functions analytic in a complex plane for plane potential fields inspire the search for the analogous efficient methods for...
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Biharmonic Problem for an Angle and Monogenic Functions
We consider a piecewise continuous biharmonic problem in an angle and the corresponding Schwartz-type boundary-value problem for monogenic functions...
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Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
The main goal of this paper is to estimate the Hölder norm of a fractal version of the Hilbert transform in the Douglis analysis context acting from...
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Commutative Complex Algebras of the Second Rank with Unity and Some Cases of Plane Orthotropy. I
Among all two-dimensional algebras of the second rank with unity e over the field of complex numbers ℂ, we find a semisimple algebra 𝔹 0 : ={ c 1 e + c 2 ω :...
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Hörmander Classes of Pseudo-Differential Operators over the Compact Group of p-Adic Integers
The purpose of this paper is to introduce new definitions of Hörmander classes for pseudo-differential operators over the compact group of p -adic...
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A Hypercomplex Method for Solving Boundary Value Problems for Biharmonic Functions
We develop a hypercomplex method of solving of boundary value problems for biharmonic functions. This method is based on a relation between...
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Some properties of a Cauchy type integral in a three-dimensional commutative algebra with one-dimensional radical
In the paper we consider a certain analog of the Cauchy type integral taking values in a three-dimensional commutative algebra over the field of...
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Discrete Pseudo-differential Operators and Applications to Numerical Schemes
We consider a class of discrete operators introduced by O. Chodosh, acting on infinite sequences and mimicking standard properties of...
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Biharmonic Monogenic Functions and Biharmonic Boundary Value Problems
We consider a commutative algebra B over the field of complex numbers with a basis {e 1, e 2} satisfying the conditions...
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Holomorphic Fourier Multipliers on Infinite Lipschitz Surfaces
It is well-known that there exists a one-one correspondence between the classical convolution singular integral operators and the Fourier multiplier...
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Schwartz-Type Boundary Value Problems for Monogenic Functions in a Biharmonic Algebra
We consider Schwartz-type boundary value problems for monogenic functions in a commutative algebra...
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Distinguished Coefficient Tensors
One of the main goals in the current volume is to employ boundary layer potential operators associated with a given second-order weakly elliptic...
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A Schwartz-type boundary value problem in a biharmonic plane
A commutative algebra B over the field of complex numbers with the bases { e 1 , e 2 } satisfying the conditions ( e 1 2 + e ...
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The Riemann–Hilbert Boundary Value Problem for the Moisil–Theodoresco System
We consider the Riemann–Hilbert boundary value problem for the Moisil–Theodoresco system in a multiply connected domain bounded by a smooth surface...
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Interior L p -Estimates for Functions in Clifford Type Algebras
In this paper we give estimates for the first order derivatives of Clifford-type algebras valued functions, in the L p -norm. As the functions are...