Results 1 to 10 of about 274,000 (205)
Pseudo-differential operators and equations in a discrete half-space
Mathematical Modelling and Analysis, 2018 We introduce a digital pseudo-differential operator acting in discrete Sobolev--Slobodetskii spaces and consider pseudo-differential equations with such operators in a discrete half-space.
Alexander V. Vasilyev +1 more
doaj +7 more sources
On discreteness of spectrum of a functional differential operator [PDF]
Mathematica Bohemica, 2014 Summary: We study conditions for the discreteness of the spectrum of the functional-differential operator \[ \mathcal {L} u=-u''+p(x)u(x)+\int_{-\infty}^\infty (u(x)-u(s))\, d_s r(x,s) \] on \((-\infty ,\infty)\). In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper, we consider a symmetric operator
Sergey Labovskiy +1 more
openalex +2 more sources
Perfect discretizations of differential operators [PDF]
, 2000 LaTeX, 20 pages, 4 ...
Simon Hauswirth
openalex +3 more sources
TA-DARTS: Temperature Annealing of Discrete Operator Distribution for Effective Differential Architecture Search [PDF]
Applied Sciences, 2023 In the realm of machine learning, the optimization of hyperparameters and the design of neural architectures entail laborious and time-intensive endeavors.
Jiyong Shin, Kyongseok Park, Dae-Ki Kang
doaj +2 more sources
Discrete differential operators in multidimensional Haar wavelet spaces [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 We consider a class of discrete differential operators acting on multidimensional Haar wavelet basis with the aim of finding wavelet approximate solutions of partial differential problems. Although these operators depend on the interpolating method used for the Haar wavelets regularization and the scale dimension space, they can be easily used to ...
Carlo Cattani, Luis Manuel Sánchez Ruiz
openalex +6 more sources
Dixmier traces for discrete pseudo-differential operators [PDF]
Journal of Pseudo-Differential Operators and Applications, 2020 In this paper we provide sharp results for the Dixmier traceability of discrete pseudo-differential operators on $\ell^2(\mathbb{Z}^n)$. In this setting, we introduce a suitable notion of a class of classical symbols which provide a class of Dixmier traceable discrete pseudo-differential operators.
Duván Cardona +2 more
openalex +5 more sources
Criteria for Discrete Spectrum of Singular Selfadjoint Differential Operators [PDF]
Proceedings of the American Mathematical Society, 1972 Under certain conditions on the coefficients of symmetric singular differential operators of order 2n, selfadjoint extensions are shown to have a discrete spectrum. The results are proven specifically for the Friedrichs extension.
L. W. Rollins
openalex +3 more sources
On discrete pseudo-differential operators and equations
Filomat, 2018 We introduce discrete pseudo-differential operators in appropriate discrete Sobolev-Slobodetskii spaces. Using discrete Fourier transform and factorization concept we study invertibility of such operators in some discrete spaces. Some examples for discrete Calderon-Zygmund operators and difference operators are considered.
Vladimir Vasilyev
openalex +5 more sources
SPLINE DISCRETE DIFFERENTIAL FORMS AND A NEW FINITE DIFFERENCE DISCRETE HODGE OPERATOR [PDF]
, 2014 We construct a new set of discrete differential forms based on B-splines of arbitrary degree as well as an associated Hodge operator. The theory is first developed in 1D and then extended to multi-dimension using tensor products.
Back, Aurore, Sonnendrücker, Eric
core +4 more sources
Non Self-Adjoint Quasi-Differential Operators with Discrete Spectra [PDF]
Rocky Mountain Journal of Mathematics, 1995 The paper investigates the spectral properties of regularly solvable operators with respect to the minimal operators \(T_0\) and \(T^+_0\) generated by a general ordinary quasi-differential expression \(M\) and its formal adjoint \(M^+\) in \(L^2(a,b)\) with a suitable weight function \(w\) \((L^2_w(a,b))\).
Sobhy El-Sayed Ibrahim
openalex +3 more sources