Related papers: The Principal Symbol Map for Lagrangian Distributi…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
We develop an $L^p(\mathbb{R}^n)$-functional calculus appropriated for interpreting "non-classical symbols" of the form $a(-\Delta)$, and for proving existence in $L^q(\mathbb{R}^n)$, some $q > p$, of solutions to nonlinear…
In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…
We compute temperate fundamental solutions of homogeneous differential operators with real-principal type symbols. Via analytic continuation of meromorphic distributions, fundamental solutions for these non-elliptic operators can be…
Noetherian operators are differential operators that encode primary components of a polynomial ideal. We develop a framework, as well as algorithms, for computing Noetherian operators with local dual spaces, both symbolically and…
In this paper, we provide proofs for the analytic characterization theorems of the operator symbols utilizing the characterization theorem for the Mittag-Leffler distribution space.We work out examples which can be interpreted as integral…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…
We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings…
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…
This paper is devoted to conducting a comprehensive and self-contained study of the boundedness on modulation spaces of Fourier integral operators arising when solving Schr\"{o}dinger type operators. The symbols of these operators belong to…
We adapt the concept of Lagrangian descriptors, which have been recently introduced as efficient indicators of phase space structures in chaotic systems, to unveil the key features of open maps. We apply them to the open tribaker map, a…
For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
For an arbitrary Riemannian manifold $X$ and Hermitian vector bundles $E$ and $F$ over $X$ we define the notion of the normal symbol of a pseudodifferential operator $P$ from $E$ to $F$. The normal symbol of $P$ is a certain smooth function…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We consider a stochastic differential equations which is driven by a Levy process. It turns out that the solution process is a Feller process if the coefficient of the SDE is bounded. Using a probabilistic formula we calculate the symbol,…