Related papers: Hyperbolic Fourier series
This paper introduces a new pseudodifferential preconditioner for the Helmholtz equation in variable media with absorption. The pseudodifferential operator is associated with the multiplicative inverse to the symbol of the Helmholtz…
We give a construction of radial Fourier interpolation formulas in dimensions 3 and 4 using Maass--Poincar\'e type series. As a corollary we obtain explicit formulas for the basis functions of these interpolation formulas in terms of what…
In this dissertation, it is first shown that, when the radial basis function is a $p$-norm and $1 < p < 2$, interpolation is always possible when the points are all different and there are at least two of them. We then show that…
We analyze the asymptotically free massless scalar $\phi^3$ quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent…
Building on the hyperboloidal foliation approach of Lefloch and Ma, we extend Klainerman's physical-space approach to dispersive estimates to recover the frequency-restricted $L^1$--$L^\infty$ dispersive estimates for Klein-Gordon…
An effective approach for construction of simple approximation for description of non-ideality effects in classical one- and two-component plasma model is under discussion. General constraints i.e. positiveness and exponential type for…
We propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses an interpolation procedure to efficiently and accurately…
We present novel microlocal and injectivity analyses of ellipsoid and hyperboloid Radon transforms. We introduce a new Radon transform, $R$, which defines the integrals of a compactly supported $L^2$ function, $f$, over ellipsoids and…
The paper discusses relations between the structure of the complex Fermi surface below the spectrum of a second order periodic elliptic equation and integral representations of certain classes of its solutions. These integral…
We propose two schemes for interpolation of the one-particle Green's function (GF) calculated within coupled-cluster singles and doubles (CCSD) method for a periodic system. They use Wannier orbitals for circumventing huge cost for a large…
The scalar Klein-Gordon equation describes wave motion in a waveguide with a cut-off. For example, the displacement of an elastic cord anchored to a solid base by elastic elements can be described by the scalar Klein-Gordon equation. We…
We give a constructive and flexible proof of a result of P. Gorkin and R. Mortini concerning a special finite interpolation problem on the unit circle with interpolating Blaschke products. Our proof also shows that the result can be…
In this study, we investigate the Klein-Gordon-Zakharov system with a focus on identifying multi-soliton solutions. Specifically, for a given number $N$ of solitons, we demonstrate the existence of a multi-soliton solution that…
Given an interpolating Blaschke product $B$ with zeros $\{a_j\}$, we seek to characterize the sequences of values $\{w_j\}$ for which the interpolation problem $$f(a_j)=w_j\qquad (j=1,2,\dots)$$ can be solved with a function $f$ from the…
We develop a method for the rigorous estimation of Hausdorff dimensions of limit sets produced by continued fraction iterated function systems. Our method is based on the approximation of a Perron-Frobenius operator using the finite element…
It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra $U_{q}(gl(2r|1)^{(2)})$ and…
We introduce the most general version of Dubrovin-type equations for divisors on a hyperelliptic curve of arbitrary genus, and provide a new argument for linearizing the corresponding completely integrable flows. Detailed applications to…
Our starting point is a lemma due to Varopoulos. We give a different proof of a generalized form this lemma, that yields an equivalent description of the $K$-functional for the interpolation couple $(X_0,X_1)$ where…
In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on Sierpinski gasket (SG). As…
We study the classical thermodynamics of a 1+1-dimensional double-well sinh-Gordon theory. Remarkably, the Schrodinger-like equation resulting from the transfer integral method is quasi-exactly solvable at several temperatures. This allows…