In mathematical analysis, Ehrenpreis's fundamental principle, introduced by Leon Ehrenpreis, states: [1]
The Huygens–Fresnel principle is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction and also reflection. It states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms the wavefront.
In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes. It was later generalized to higher-dimensional Euclidean spaces, and more broadly in the context of integral geometry. The complex analogue of the Radon transform is known as the Penrose transform. The Radon transform is widely applicable to tomography, the creation of an image from the projection data associated with cross-sectional scans of an object.
In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics.
Frigyes Riesz was a Hungarian mathematician who made fundamental contributions to functional analysis, as did his younger brother Marcel Riesz.
In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simple functions.
In queueing theory, a discipline within the mathematical theory of probability, Kendall's notation is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953 where A denotes the time between arrivals to the queue, S the service time distribution and c the number of service channels open at the node. It has since been extended to A/S/c/K/N/D where K is the capacity of the queue, N is the size of the population of jobs to be served, and D is the queueing discipline.
Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size.
In mathematics, the Malgrange–Ehrenpreis theorem states that every non-zero linear differential operator with constant coefficients has a Green's function. It was first proved independently by Leon Ehrenpreis and Bernard Malgrange (1955–1956).
Eliezer 'Leon' Ehrenpreis was a mathematician at Temple University who proved the Malgrange–Ehrenpreis theorem, the fundamental theorem about differential operators with constant coefficients.
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
In mathematics, precisely in the theory of functions of several complex variables, Hartogs's extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that the support of the singularities of such functions cannot be compact, therefore the singular set of a function of several complex variables must 'go off to infinity' in some direction. More precisely, it shows that an isolated singularity is always a removable singularity for any analytic function of n > 1 complex variables. A first version of this theorem was proved by Friedrich Hartogs, and as such it is known also as Hartogs's lemma and Hartogs's principle: in earlier Soviet literature, it is also called Osgood–Brown theorem, acknowledging later work by Arthur Barton Brown and William Fogg Osgood. This property of holomorphic functions of several variables is also called Hartogs's phenomenon: however, the locution "Hartogs's phenomenon" is also used to identify the property of solutions of systems of partial differential or convolution equations satisfying Hartogs type theorems.
Sigurður Helgason is an Icelandic mathematician whose research has been devoted to the geometry and analysis on symmetric spaces. In particular he has used new integral geometric methods to establish fundamental existence theorems for differential equations on symmetric spaces as well as some new results on the representations of their isometry groups. He also introduced a Fourier transform on these spaces and proved the principal theorems for this transform, the inversion formula, the Plancherel theorem and the analog of the Paley–Wiener theorem.
Pavel Grinfeld is a mathematician and associate professor of Applied Mathematics at Drexel University working on problems in moving surfaces in applied mathematics, geometry, physics, and engineering.
In science and engineering, an intrinsic property is a property of a specified subject that exists itself or within the subject. An extrinsic property is not essential or inherent to the subject that is being characterized. For example, density is an intrinsic property of any physical object, whereas weight is an extrinsic property that depends on another object.
Robert Ralph Phelps was an American mathematician who was known for his contributions to analysis, particularly to functional analysis and measure theory. He was a professor of mathematics at the University of Washington from 1962 until his death.
Dragoslav D. Šiljak is Professor Emeritus of Electrical Engineering at Santa Clara University, where he held the title of Benjamin and Mae Swig University Professor.
Jürgen Jost is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.
Kathryn Elizabeth Hare is a Canadian mathematician specializing in harmonic analysis and fractal geometry. She is the Chair of the Pure Mathematics Department at the University of Waterloo.
Not to be confused with Alexander Nagel, art historian and professor at NYU.
Alexander Joseph Nagel is an American mathematician, specializing in harmonic analysis, functions of several complex variables, and linear partial differential equations.
Dorina Irena-Rita Mitrea is a Romanian-American mathematician known for her work in harmonic analysis, partial differential equations, and the theory of distributions, and in mathematics education. She is a professor of mathematics and chair of the mathematics department at Baylor University.
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