Compact Support Function Example

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Compact Support -- from Wolfram MathWorld

    http://mathworld.wolfram.com/CompactSupport.html
    Jan 02, 2020 · A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For example, the function f:x->x^2 in its entire domain (i.e., f:R->R^+) does not have compact support, while any bump function does have compact support.

Function of compact support - Encyclopedia of Mathematics

    https://www.encyclopediaofmath.org/index.php/Function_of_compact_support
    The support of is the closure of the set of points for which is different from zero . Thus one can also say that a function of compact support in is a function defined on such that its support is a closed bounded set located at a distance from the boundary of by a number greater than , where is sufficiently small.

Support (mathematics) - Wikipedia

    https://en.wikipedia.org/wiki/Compact_support
    For example, if f : [0,1] → R is the Dirichlet function that is 0 on irrational numbers and 1 on rational numbers, and [0,1] is equipped with Lebesgue measure, then the support of f is the entire interval [0,1], but the essential support of f is empty, since f is equal almost everywhere to the zero function.

Lecture 14 - MIT OpenCourseWare

    https://ocw.mit.edu/courses/mathematics/18-101-analysis-ii-fall-2005/lecture-notes/lecture14.pdf
    3.9 Support and Compact Support Now for some terminology. Let U be an open set in Rn, and let f : U → R be a continuous function. Definition 3.26. The support of fis supp f= x∈ U: f(x) = 0}. (3.164) For example, supp f Q = Q. Definition 3.27. Let f : U → R be a continuous function. The function f is compactly supported if supp fis ...

analysis - example of a function with compact support ...

    https://math.stackexchange.com/questions/284045/example-of-a-function-with-compact-support
    Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …

Bump function - Wikipedia

    https://en.wikipedia.org/wiki/Bump_function
    Examples. The function : → given by = {⁡ (− −), ∈ (−,),is an example of a bump function in one dimension. It is clear from the construction that this function has compact support, since a function of the real line has compact support if and only if it has bounded and closed support.

An example of an infinitely differentiable function with ...

    https://math.stackexchange.com/questions/1283783/an-example-of-an-infinitely-differentiable-function-with-compact-support
    Could anyone give me a function infinitely differentiable on the real line and having a compact support? And the function must be nonnegative and normalized, i.e. the integration of the function on the real line must be one. I tried to think of one myself, but it seems trickier than expected.

(PDF) Continuous functions with compact support

    https://www.researchgate.net/publication/259260858_Continuous_functions_with_compact_support
    We show, in particular, that for continuous frames, the pointfree rings of continuous functions with compact support are Noetherian if and only if the underlying set of the frame is finite; see ...

Compact support vector machine regression model - MATLAB

    https://www.mathworks.com/help/stats/classreg.learning.regr.compactregressionsvm-class.html
    Description. CompactRegressionSVM is a compact support vector machine (SVM) regression model. It consumes less memory than a full, trained support vector machine model (RegressionSVM model) because it does not store the data used to train the model.Because the compact model does not store the training data, you cannot use it to perform certain tasks, such as cross validation.



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