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gptkbp:instanceOf
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Integral Transform
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gptkbp:application
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gptkb:Number_Theory
Image Analysis
Asymptotic Analysis
Solution of Differential Equations
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gptkbp:category
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gptkb:Mathematical_Analysis
Transforms
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gptkbp:defines
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The Mellin transform of a function f(x) is defined as M{f}(s) = ∫₀^∞ x^{s-1} f(x) dx.
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gptkbp:domain
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Functions on (0, ∞)
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gptkbp:field
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gptkb:Mathematics
gptkb:Complex_Analysis
Harmonic Analysis
Integral Transforms
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gptkbp:firstPublished
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1897
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gptkbp:generalizes
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Two-sided Laplace Transform
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https://www.w3.org/2000/01/rdf-schema#label
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Mellin Transform
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gptkbp:inverseTransform
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Inverse Mellin Transform
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gptkbp:namedAfter
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gptkb:Hjalmar_Mellin
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gptkbp:notation
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M{f}(s)
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gptkbp:property
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gptkb:Parseval's_Theorem
Linearity
Convolution Theorem
Scaling Property
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gptkbp:range
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Complex Plane
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gptkbp:relatedTo
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gptkb:Fourier_Transform
gptkb:Laplace_Transform
gptkb:Z-Transform
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gptkbp:usedIn
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gptkb:Signal_Processing
gptkb:Optics
Statistics
Analysis of Algorithms
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gptkbp:bfsParent
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gptkb:Laplace_Transform
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gptkbp:bfsLayer
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6
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