This article is about hyperfunctions in a mathematical context. For biological hypo- or hyperfunctions, see endocrine disease.
In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato in 1958 in Japanese, (1959, 1960 in English), building upon earlier work by Laurent Schwartz, Grothendieck and others.
In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought...
Adrenocortical hyperfunction is a condition where there is an overexpression of products of the adrenal cortex. When cortisol is overproduced, it is called...
analysis to study properties and generalizations of functions such as hyperfunctions and microfunctions. Semantically, it is the application of algebraic...
(such as in hemolytic anemias), which suggests that it is a response to hyperfunction. It is therefore not surprising that splenomegaly is associated with...
be caused by an abnormal dental eruption (delayed passive eruption), hyperfunction of the upper lip elevator muscle, excessive vertical growth of the maxilla...
Hypergonadism is a condition where there is a hyperfunction of the gonads. It can manifest as precocious puberty, and is caused by abnormally high levels...
of reserve, hyposecretion, agenesis, atrophy, or active destruction. Hyperfunction can occur as a result of hypersecretion, loss of suppression, hyperplastic...
mathematician known for founding the fields of algebraic analysis, hyperfunctions, and holonomic quantum fields. He was a professor at the Research Institute...
will be the same. The Heaviside step function can be represented as a hyperfunction as H ( x ) = ( 1 − 1 2 π i log z , − 1 2 π i log z ) . {\displaystyle...
folds is hyperfunctional. Hyperfunction may also make it difficult to detect the presence of vocal fold paresis. Hyperfunction of the area above the vocal...
small-group version was released as Reuter's Todmorden 513 album on the Hyperfunction label in 2011. The 2013 orchestral version has been recorded and released...
of reserve, hyposecretion, agenesis, atrophy, or active destruction. Hyperfunction can occur as a result of hypersecretion, loss of suppression, hyperplastic...
schizophrenia is still poorly understood, a number of factors, such as dopamine hyperfunction, glutamatergic hypofunction, GABAergic deficits, cholinergic system...
diagnostic performance. Primary hyperparathyroidism results from a hyperfunction of the parathyroid glands themselves. The oversecretion of PTH is due...
convolution algebras that are integral domains; and the theories of hyperfunctions, based (in their initial conception) on boundary values of analytic...
difference of the limits of F± from the appropriate half-planes, or as a hyperfunction distribution. Two functions of this form are a solution of the Riemann–Hilbert...
Jonathan Cape. p. 471. Penrose, R (2004). "9: Fourier decompositions and hyperfunctions". The Road to Reality. Jonathan Cape. Physical Sciences. Encyclopædia...
about the causes of aging, the programmatic theory (also known as the hyperfunction theory, and the developmental theory). This was developed by George...
Mikio Sato Japan for his creation of algebraic analysis, including hyperfunction theory and microfunction theory, holonomic quantum field theory, and...
546–551. Original French text. Komatsu, Hikosaburo (2002). "Fourier's hyperfunctions and Heaviside's pseudodifferential operators". In Takahiro Kawai; Keiko...
old age, which supports the notion that antagonistic pleiotropy or "hyperfunction" drives human aging. Chronic iron toxicity is usually the result of...
common site for injury. If a person has a phonotrauma or habitual vocal hyperfunction, also known as pressed phonation, the proteins in the basal lamina can...
Vocal overuse (speaking for long periods), abuse (yelling), or misuse (hyperfunction) may produce excessive amounts of mechanical stress by increasing the...
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