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The Fredholm alternative is the statement that, for every non-zero fixed complex number, either the first equation has a non-trivial solution, or the second equation has a solution for all (). A sufficient condition for this statement to be true is for K ( x , y ) {\displaystyle K(x,y)} to be square integrable on the rectangle [ a , b ] × [ a ...
In mathematics, Fredholm solvability encompasses results and techniques for solving differential and integral equations via the Fredholm alternative and, more generally, the Fredholm-type properties of the operator involved. The concept is named after Erik Ivar Fredholm. Let A be a real n × n-matrix and a vector
On 16 December 2017, former President Jacob Zuma announced that "fully subsidised free higher education and training for poor and working class South African students" would be phased in by the South African government over a period of five years. [15] In March 2021, the NSFAS announced that its funding was insufficient to fund first-year students.
Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory of Hilbert spaces. Biography [ edit ]
In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space.
AIMS South Africa is sponsored by international corporations, international development organisations and the South African departments of Education and Science and Technology. In February 2010, Google donated $1 million to AIMS. [21] In July 2010, Canada committed CAN$20 million of federal funding to AIMS and the AIMS-Next Einstein Initiative.
In mathematics, Fredholm's theorems are a set of celebrated results of Ivar Fredholm in the Fredholm theory of integral equations. There are several closely related theorems, which may be stated in terms of integral equations, in terms of linear algebra , or in terms of the Fredholm operator on Banach spaces .
In mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations.They are named in honour of Erik Ivar Fredholm.By definition, a Fredholm operator is a bounded linear operator T : X → Y between two Banach spaces with finite-dimensional kernel and finite-dimensional (algebraic) cokernel = / , and with closed range .