MOLLIFIER Meaning and
Definition
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A mollifier is a mathematical function that is utilized in the field of harmonic analysis and measure theory to smooth out or soften another function. It is typically a continuous, non-negative function that is integrable, i.e., it has a finite area under its graph.
The main purpose of a mollifier is to approximate a given function by a smoother one. This is achieved by convolving the mollifier with the original function. Convolution involves applying the mollifier to each point of the original function, effectively "blurring" or "smoothing" the function in a controlled manner. By adjusting the size and shape of the mollifier, different degrees of smoothing can be achieved.
Mollifiers are commonly used in the study of singularities and irregularities in functions, as they have the ability to remove or decrease these problematic points while preserving the overall properties of the function. They are widely employed in signal processing, image analysis, and differential equations, among other areas of mathematics and engineering.
It is important to note that mollifiers are not intended to modify or alter the underlying properties or behavior of a function, but rather to provide an approximate representation that is more amenable to analysis and calculations.
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One who or that which softens or appeases.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
Common Misspellings for MOLLIFIER
Etymology of MOLLIFIER
The word "mollifier" originates from the Latin verb "mollificare", which is derived from two Latin roots: "mollis", meaning soft or gentle, and "facere", meaning to make or do. This combination translates to "to make soft or gentle". Over time, the word "mollifier" was adopted into Middle English, maintaining the same meaning. It is commonly used as a noun or a verb to describe someone or something that soothes or calms another person or situation.
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